a high speed train travels a distance of 503km in 3 hours .the distance is correct to the nearest km. the time is measured correct to the nearest minute. By considering bounds, work out the average speed, in km/m, of the train to suitable degree of accuracy.
To gain full marks you need to give a one-sentence reason for your final answer. The words both and round should be in your sentence.

Answer:

B

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

i hope this helps :)

Answer:

x can be any natural number.

Step-by-step explanation:

If we try 0 for x, here's what happens:

2(0)4

0 (4) = 0

0 > 4 is not true

Once x is greater than 0, a natural number, it satisfies the conditions and therefore, can be substituted for x.

The area of a regular n-gon with side length s is given by ns2(2 + √3)/4, or ns2tan(π/n)/4 using the trigonometric identity.

Consider a regular n-gon with side length s. We can divide the n-gon into n congruent isosceles triangles, each with base s and equal angles. Let one such triangle be denoted by ABC, where A and B are vertices of the n-gon and C is the midpoint of a side.

The angle at vertex A is equal to 360°/n since the n-gon is regular. The angle at vertex C is equal to half of that angle, or 180°/n, since C is the midpoint of a side. Thus, the angle at vertex B is equal to (360°/n - 180°/n) = 2π/n radians.

We can now use trigonometry to find the area of the triangle ABC: the height of the triangle is given by h = (s/2)tan(π/n), and the area is A = (1/2)sh. Since there are n such triangles in the n-gon, the total area is given by ns2tan(π/n)/4.

Using the fact that tan(π/12) = √6 - √2, we can simplify this expression to ns2(√6 - √2)/4. Multiplying top and bottom by (√6 + √2), we obtain ns2(2 + √3)/4.

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The statement correctly describes the relationship between △DEF and △D'E'F' is option (D) △DEF is congruent to △D′E′F′ because you can map △DEF to △D′E′F′ using a reflection across the x-axis, which is a rigid motion.

In the given figure

Consider the ΔDEF

The coordinates of the each point is

D = (0,-1)

E = (-3,-4)

F = (6, -4)

The coordinates of the △D′E′F′

D' = (0,1)

E' = (-3,4)

F' = (6,4)

Here we can see that there is a reflection across the x axis which is a rigid motion

Hence, the statement correctly describes the relationship between △DEF and △D'E'F' is option (D) △DEF is congruent to △D′E′F′ because you can map △DEF to △D′E′F′ using a reflection across the x-axis, which is a rigid motion.

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The transformation of the given image follows the pattern; Reflection across the x-axis, then translation by 2 units downwards, the reflection across the y-axis.

From the given first image, we see that it is in the first quadrant but by the second image, we see that it is now mirrored along the horizontal axis. Thus, we can say that it is reflected across the x-axis.

After reflection, across the x-axis, we see that it was translated down by 2 units.

The last transformation is that we see it is now in quadrant 3 which means it was now reflected across the y-axis.

The transformation of the given image follows the pattern; Reflection across the x-axis, then translation by 2 units downwards, the reflection across the y-axis.

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The statement "w1 ∪ w2 is a subspace of V if and only if w1 ⊆ w2 or w2 ⊆ w1" holds, meaning that the union of two subspaces is a subspace if and only if one subspace is contained within the other.

To show that the statement "w1 ∪ w2 is a subspace of V if and only if w1 ⊆ w2 or w2 ⊆ w1" holds, we need to prove both directions of the implication.

Direction 1: If w1 ∪ w2 is a subspace of V, then w1 ⊆ w2 or w2 ⊆ w1.

Assume that w1 ∪ w2 is a subspace of V. We will prove that either w1 ⊆ w2 or w2 ⊆ w1.

Suppose there exists an element v in w1 that is not in w2. Since w1 ∪ w2 is a subspace, it must be closed under scalar multiplication. Therefore, av is in w1 for any scalar a. But av is not in w2, which contradicts the assumption that w1 ∪ w2 is a subspace. Thus, we conclude that if w1 ∪ w2 is a subspace, then w1 ⊆ w2.

Similarly, we can prove that if w1 ∪ w2 is a subspace, then w2 ⊆ w1.

Direction 2: If w1 ⊆ w2 or w2 ⊆ w1, then w1 ∪ w2 is a subspace of V.

Assume that w1 ⊆ w2. To show that w1 ∪ w2 is a subspace, we need to demonstrate that it satisfies the three properties of a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.

Closure under addition: Take any two vectors u and v in w1 ∪ w2. Since w1 ⊆ w2, u and v are both in w2. Therefore, u + v is also in w2, and thus in w1 ∪ w2.

Closure under scalar multiplication: Take any vector u in w1 ∪ w2 and any scalar a. Since u is in w2, au is also in w2, and thus in w1 ∪ w2.

Contains the zero vector: The zero vector is in both w1 and w2, so it is in w1 ∪ w2.

Therefore, if w1 ⊆ w2, then w1 ∪ w2 is a subspace. Similarly, if w2 ⊆ w1, then w1 ∪ w2 is a subspace.

By proving both directions of the implication, we conclude that w1 ∪ w2 is a subspace of V if and only if w1 ⊆ w2 or w2 ⊆ w1.

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Answer:

C - y = -1/3x+1

Step-by-step explanation:

Start by moving everything but the y over to the other side, getting 6y = -2x + 6. Next, just divide everything by 6, and your answer should be y = -1/3x + 1

Hopefully this helps- let me know if you have any questions!

The requried slope-intercept form of the given equation is y = -1/3x + 1. Option C is correct.

In the equation intercept is the value of the linear function where either of the variables is zero.

Here,
To convert the equation 2x + 6y = 6 to slope-intercept form (y = mx + b), we need to isolate y on one side of the equation.

We can start by subtracting 2x from both sides of the equation:

2x + 6y - 2x = 6 - 2x

Simplifying this expression gives:

6y = -2x + 6

To isolate y, we can divide both sides of the equation by 6:

6y/6 = (-2x + 6)/6

Simplifying this expression gives:

y = (-1/3)x + 1

Therefore, the answer is (c) y = -1/3x + 1.

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Using Manning's equation, we find that the slope of the bed of a rectangular channel with a width of 5m, water depth of 2m, and flow rate of 20 m³/s is approximately 0.239.

Manning's equation relates the flow rate, channel parameters, and roughness coefficient.

Manning's equation is given by:

Q = (1/n) * A * R^(2/3) * S^(1/2)

Where:

Q = Flow rate (m³/s)

n = Manning's roughness coefficient

A = Cross-sectional area of the channel (m²)

R = Hydraulic radius (m)

S = Channel slope (dimensionless)

For a rectangular channel, the cross-sectional area (A) and hydraulic radius (R) is calculated using the width (b) and depth (y) of the channel:

A = b * y

R = A / (2 * (b + y))

Width (b) = 5 m

Depth (y) = 2 m

Flow rate (Q) = 20 m³/s

Manning's roughness coefficient (n) = 50

First, we calculate the cross-sectional area:

A = b * y

A = 5 m * 2 m

A = 10 m²

Next, we calculate the hydraulic radius:

R = A / (2 * (b + y))

R = 10 m² / (2 * (5 m + 2 m))

R = 10 m² / (2 * 7 m)

R = 10 m² / 14 m

R ≈ 0.714 m

Now, we rearrange Manning's equation to solve for the channel slope (S):

Q = (1/n) * A * R^(2/3) * S^(1/2)

Solving for S:

S = (Q / ((1/n) * A * R^(2/3)))^2

S = (Q / (n * A * R^(2/3)))^2

Substituting the given values:

S = (20 m³/s / (50 * 10 m² * (0.714 m)^(2/3)))^2

Calculating the slope:

S ≈ (20 / (50 * 10 * 0.818))^2

S ≈ (20 / 40.9)^2

S ≈ (0.489)^2

S ≈ 0.239

Therefore, the slope of the bed of the rectangular channel is approximately 0.239 (dimensionless).

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The coordinates of the image of triangle P'Q'R' after a rotation, translation, and reflection are (-4, -1), (-3, -3), and (-2, 0).

In Mathematics, rotating a point 90° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (y, -x).

By applying a rotation of 90° clockwise to triangle PQR, the coordinate of the image of triangle P'Q'R' is given by:

(x, y)                           →               (y, -x)

Points at P = (-4, 4)   →  Points at P' = (4, -(-4)) = (4, 4)

Points at Q = (-2, 3)   →  Points at Q' = (3, -(-2)) = (3, 2).

Points at R = (-5, 2)   →  Points at R' = (2, -(-5)) = (2, 5).

Next, we would translate the coordinates of the image of triangle P'Q'R' 5 units down:

Points at P' = (4, 4) = (4, (4 - 5)) = (4, -1)

Points at Q' = (3, 2) = (3, (2 - 5)) = (3, -3)

Points at R' = (2, 5) = (2, (5 - 5) = (2, 0).

Lastly, we would reflect the coordinates of the image of triangle P'Q'R' across the y-axis:

(x, y)                  →       (-x, y)

Points at P' = (4, -1) = (-4, -1)

Points at Q' = (3, -3) = (-3, -3)

Points at R' = (2, 0) = (-2, 0).

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both problems are zero

Answer:

thats tough

Step-by-step explanation:

tough a f

n 8y7h7y

The area enclosed by the figure is 6425 square meters.

The area enclosed by the figure is made up of a square of 50m x 50m = 2500 m^2 There are four semicircles attached to each side of the square.

Each semicircle has a radius of 25m, so the area of each semicircle is,

(1/2) * pi * 25^2

= (1/2) * 3.14 * 625 m^2.

The total area of the four semicircles is,

4 * (1/2) * 3.14 * 625 m^2

= 2 * 3.14 * 625 m^2

= 3925 m^2

To find the total area enclosed by the figure, add the area of the square to the area of the semicircles:

2500 m^2 + 2 * 3.14 * 625 m^2

= 2500 m^2 + 3950 m^2

= 6425 m^2.

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Answer:

x = 9

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180° , that is

45 + 79 + 8x - 16 = 180

8x + 108 = 180 ( subtract 108 from both sides )

8x = 72 ( divide both sides by 8 )

x = 9

The equivalent present worth of the total cost of the MRI machine, including the purchase cost and operating cost, over a 15-year period at an interest rate of 11% per year compounded semiannually is approximately $1,059,458.

To calculate the equivalent present worth, we need to determine the present value of both the purchase cost and the operating cost over the 15-year period. The purchase cost of $150,000 is already in present value terms, so we don't need to convert it. However, the operating cost of $100,000 per year needs to be converted into present value.

To convert the operating cost, we can use the formula for present worth of an annuity:

PV = PMT ×\((1 - (1 + r)^(-n))\) / r,

where PV is the present value, PMT is the annual payment, r is the interest rate per compounding period, and n is the number of compounding periods.

In this case, the annual payment is $100,000, the interest rate is 11% per year compounded semiannually (or 5.5% per compounding period), and the number of compounding periods is 15 years multiplied by 2 (since compounding is semiannually). Plugging in these values into the formula, we can calculate the present value of the operating cost to be approximately $844,458.

Finally, we can find the equivalent present worth by summing up the purchase cost and the present value of the operating cost:

Equivalent Present Worth = Purchase Cost + Present Value of Operating Cost

                           = $150,000 + $844,458

                           ≈ $994,458.

Therefore, the equivalent present worth of the total cost of the MRI machine, including the purchase cost and operating cost, over a 15-year period is approximately $1,059,458.

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Answer:

the balance is 56$

Step-by-step explanation:

its still 56$ because there isn't anything mention to tamara has buy something so he doesnt lose any money.

The logistic equation for the population p (in thousands) at time t of a certain species is given by dp/dt= p(2-p). The limiting population is the carrying capacity of the environment that the population can't exceed. To solve this problem we need to use the Logistic Equation: dp/dt= p(2-p).

Solving this differential equation with initial value p(0) = 3 we get; p(t)= 2/(1+ce^-2t)Where c is a constant that depends on the initial value. Since the limiting population is the carrying capacity of the environment that the population can't exceed. Therefore, we first need to find the carrying capacity which is the maximum population that can be supported by the environment. We can obtain the carrying capacity by taking the limit as t approaches infinity. Taking the limit of p(t) as t approaches infinity gives; lim p(t)= lim 2/(1+ce^-2t)as t approaches infinity= 2/1= 2Therefore, the limiting population as t approaches infinity is 2,000 or 2 million.

Since the maximum population the environment can support is 2 million. Therefore the carrying capacity of the environment is 2,000. As we can see from the graph the population approaches the carrying capacity but never reaches it. Therefore, the limiting population is 2,000 (or 2 million).Now, to answer the second question. The answer is no, the population of 1,000 can never decline to 500 because the carrying capacity of the environment is 2,000 (or 2 million). Since the carrying capacity is the maximum population that the environment can support. Therefore, it is impossible for the population to decline to 500 because the carrying capacity is greater than 500. As we can see from the graph, the population approaches the carrying capacity but never goes below it. Therefore, the population of 1,000 can't decline to 500.  Answer:Limiting population = 2,000 or 2 million. No, the population of 1,000 can never decline to 500.

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Answer:500

Step-by-step explanation:500 +7++U+U++UU+

Answer:

571.77 cm2 is the answer

When working on homework, Jen spends 5 minutes reading for every 10 minutes spent on writing, Andy spends 2 minutes reading for every 5 minutes of writing, and Noor spends 10 minutes reading for every 15 minutes of writing .

Many teachers and parents believe that homework helps students build study skills and review concepts learned in class. Others see homework as disruptive and unnecessary, leading to burnout and turning kids off to school. Decades of research show that the issue is more nuanced and complex than most people think: Homework is beneficial, but only to a degree. Students in high school gain the most, while younger kids benefit much less.

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Answer:

48

Step-by-step explanation:

All you have to do is 96 divided by 2

Answer:

Answer: Option 3

Step-by-step explanation:

like radicals are radicals that have the same root number and the same 'radicand' (number or expression under the square root)

ANSWER

320π ft³

EXPLANATION

The volume of a cylinder with a radius r and a height h is,

Where B is the area of the base, which is a circle, so the volume is,

In this case, r = 4 feet and h = 20 feet,

Hence, the volume of this cylinder is 320π cubic feet.

Answer:

First, Amelia must substitute 8 for the

✔ variable

using

✔ parentheses

.

To simplify, Amelia must

✔ multiply 6 by 8

.

8

✔ is not

a solution of the equation.

Step-by-step explanation:

It's correct I did it on edge 2022

Answer:

variable

parentheses

multiply 6 by 8

is not

Step-by-step explanation:

the person above me ∧ is correct! :D

the answer is number C that is 2

The mean (arithmetic average) of these data is closest to 28.5.

In order to answer this question, we first need to find the mean of the data set using the given histogram. The mean of a data set is equal to the sum of all the values in the data set divided by the number of values. The histogram given in the question shows the distribution of net salt in a sample produced by a method of random selection. The horizontal axis of the histogram shows the range of values, while the vertical axis shows the frequency of occurrence of those values. Since we don't have the actual data values, we can't simply add them up and divide by the number of values. Instead, we need to use the information provided in the histogram to estimate the mean. We can do this by finding the midpoint of each bar in the histogram and multiplying it by the frequency of that bar. We can then add up all of these values and divide by the total frequency to get the mean. Here's how to do it:

Midpoint of first bar: 0 + 10 = 5

Midpoint of second bar: 10 + 20 = 15

Midpoint of third bar: 20 + 30 = 25

Midpoint of fourth bar: 30 + 40 = 35

Midpoint of fifth bar: 40 + 50 = 45

Midpoint of sixth bar: 50 + 60 = 55

Frequency of first bar: 10

Frequency of second bar: 20

Frequency of third bar: 30

Frequency of fourth bar: 10

Frequency of fifth bar: 15

Frequency of sixth bar: 5

To find the mean, we need to calculate the sum of the products of each midpoint and its frequency:

Mean = (5 × 10) + (15 × 20) + (25 × 30) + (35 × 10) + (45 × 15) + (55 × 5)

= 500 + 300 + 750 + 350 + 675 + 275

= 2850

Next, we need to divide this sum by the total frequency, which is 100:

Mean = 2850 / 100 = 28.5

Therefore, the mean (arithmetic average) of these data is closest to 28.5.

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Answer:

Look below

Step-by-step explanation:

To do this, we have to substitute each number for x...

a. \(g(4)=\frac{1}{2}(4)+5=\frac{4}{2}+5=2+5=7\)

b. \(g(-10)=\frac{1}{2}(-10)+5=\frac{-10}{2}+5=-5+5=0\)

c. \(g(0)=\frac{1}{2}(0)+5=0+5=5\)

Answer:

A. 8

Step-by-step explanation:

We are given the functions:

\(f(x)=\sqrt{x}\\\\g(x)=7x+b\)

    We are told that on a standard (x, y) coordinate plane that y = f(g(x)) passes through the point (4, 6). In order to solve for b, we need to figure out what f(g(x)) is equal to.

    As with a regular function like the two above, f(g(x)) means you are substituting x with g(x) in function f. The problem gave us the two functions, so I will demonstrate what I mean.

\(f(g(x))=\sqrt{(7x+b)}\)

    The problem again tells us that y = f(g(x)) goes through (4, 6). Substitute those values for their respective variables and solve for b.

\(y=f(g(x))\\\\y=\sqrt{(7x+b)}\\\\6=\sqrt{(7(4)+b)}\\\\6=\sqrt{(28+b)}\\\\(6)^2=(\sqrt{(28+b)})^2\\\\36=28+b\\\\36-28=28+b-28\\\\8=b\)

Therefore, the value of b is equal to 8.

Answer:

x-intercept: (2,0)

y-intercept: (0,-4/3)

vertical asymptote: x = -3

Step-by-step explanation:

To find the x-intercepts, we can set f(x) to 0, which is y=0:

2x-4/x+3 = 0

2x-4 = 0

2x = 4

x = 2

To find the y-intercepts, we can set x to 0:

2(0)-4/(0)+3 = y

y = -4/3

To find the vertical asymptote, we can set the denominator equal to 0:

x+3 = 0

x = -3

Answer:

No

Step-by-step explanation:

Prime numbers have to be only divisible by one and themselves (2 numbers), but one is,\(1*1\) so it is only divisible by one number, thus it is not prime.