A train travelling at 30km/hour reaches a tunnel which is 9 times as long as the train. If the train takes 2 minutes to completely clear the tunnel, how long is the train?​

Answer:

0.6192

Step-by-step explanation:

Answer:

Last option

....... -0.4

Answer:

22/7 is not pi

Step-by-step explanation:

22/7 is just a close approximation for pi, not pi itself.

If you put 22/7 into a calculator, you get:

3.142857...

While the number pi itself is:

3.1415926...

You can notice that pi is actually different than 22/7, even though the two numbers start out the same and are close to each other. Frequently in geometry, you use 22/7 as pi because it's so close and makes calculation easier.

Hope this helps!

Answer:

by observation we get to know

highest is 28

lowest is 4

hence difference = 28 - 4 = 24

brainliest plsss

Answer:

Answer is option C

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

Step-by-step explanation:

Given:

Isolate b:

Find b:

[tex]\\ \sf\longmapsto t+\dfrac{1}{2}b=Y[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{2}b=Y-t[/tex]

[tex]\\ \sf\longmapsto \dfrac{b}{2}=Y-t[/tex]

[tex]\\ \sf\longmapsto b=2(Y-t)[/tex]

[tex]\\ \sf\longmapsto b=2Y-2t[/tex]

Step-by-step explanation:

1/(seca-tana) - 1/cosa=1/cosa -1/(seca+tana)

There are many ways to solve this, let's take a look at a simple one

1/(seca-tana) + 1/(seca+tana) =1/cosa + 1/cosa

((seca-tana)+(seca+tana))/(sec^2a-tan^2a)=2/cosa

(seca-tana+seca+tana)/1=2*1/cosa

2seca=2seca

Answer:

Mapping C represents a function.

To be a function, there must be one and only one y value (output) for every input value (x value).

Mapping C matches this criteria, thus it is a function.

Let me know if this helps!

Answer:

470

Step-by-step explanation:

2(7×2+2×2+2×7)+2(12×7+7×7+12×7)-2(7×2)

= 64+434-28

= 470 cm²

Answer:

Parallel: AC and DB, BA and CD

Perpendicular: AC and CD, DB and CD, DB and BA, BA and AC

Neither: None

Step-by-step explanation:

Step 1: Find Slopes

Let's first find the slopes of each side of the rectangle, as that will helps us determine which sides are parallel, perpendicular, or neither.

Recall that the formula for finding the slope between two points is [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex] where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the two points. To avoid confusion, I will be taking the first point I list as [tex](x_1,y_1)[/tex] and the second point as [tex](x_2,y_2)[/tex].

Slope of [tex]BA[/tex]:

[tex]\frac{-7-(-3)}{-1-(-4)}\\=\frac{-7+3}{-1+4} \\= -\frac{4}{3}[/tex]

Slope of [tex]AC[/tex]:

[tex]\frac{-4-(-7)}{3-(-1)} \\=\frac{-4+7}{3+1} \\=\frac{3}{4}[/tex]

Slope of [tex]CD[/tex]:

[tex]\frac{0-(-4)}{0-3} \\=\frac{4}{-3} \\=-\frac{4}{3}[/tex]

Slope of [tex]DB[/tex]:

[tex]\frac{-3-0}{-4-0} \\=\frac{-3}{-4} \\=\frac{3}{4}[/tex]

Step 2: Determine which sides are parallel, perpendicular, or neither

Now that we found the slopes of the sides, we can determine which sides are parallel, perpendicular, or neither.

Recall that parallel lines have the same slope. [tex]\bf AC[/tex] and [tex]\bf DB[/tex], along with [tex]\bf BA[/tex]and [tex]\bf CD[/tex], have the same slope, so they are parallel. No other pair of sides has the same slope, so these are our only parallel pairs.

For two lines to be perpendicular, the product of their slopes must be [tex]-1[/tex]. [tex]\bf AC[/tex] and [tex]\bf CD[/tex], [tex]\bf DB[/tex] and [tex]\bf CD[/tex], [tex]\bf DB[/tex] and [tex]\bf BA[/tex], and [tex]\bf BA[/tex] and [tex]\bf AC[/tex] [tex]\bf[/tex]meet that criteria, so they are perpendicular. No other pair of sides meets the criteria, so these are our only perpendicular pairs. Hope this helps!

Answer:

30

Step-by-step explanation:

The total number of people is

5+6+4+7+5+3 = 30 people

Answer:

30

Step-by-step explanation:

pizza:5+7=12

Burger:6+5=11

Other:4+3=7

Total:12+11+7=30

Answer:

57/5

Step-by-step explanation:

what is that supposed to be ?

1.5 + 9.9 ?

I base my answer in that assumption.

1.5 = 3/2

9.9 = 99/10

so, we need 3/2 + 99/10.

how do we do that ?

by bringing both fractions to the same denominator (bottom parts) but without changing the value of the fractions. that means we need to multiply numerator and denominator (top and bottom parts) by the same factor. and that factor is determined by what is needed to transform the denominator.

we have denominators 2 and 10. what is the smallest common multiple ?

I think it is plainly visible : 10. as 2 also cleanly divides 10.

in other examples, if you don't see that right away, the simplest approach is to just multiply both denominators (in our case 2×10 = 20) and work with that result.

so, we are trying to bring both fractions to denominators of 10 (or, as mentioned 20), so that we can easily add the fractions.

let's start with 3/2.

what multiplication do we need to do to turn 2 into 10 ?

right, by multiplying by 5.

remember, we need to do the same thing to numerator and denominator to keep the value of the fraction unchanged.

so, we do the following

3/2 × 5/5

as you can see, multiplying something by 5/5 does not change any value, as it means we are just multiply by 1. but we can use that little trick to change the appearance of the original fraction.

so,

3/2 × 5/5 = (3×5) / (2×5) = 15/10

by the way, if we had wanted to change the denominator to 20, our factor would have been 10/10, and we would have gotten 30/20.

now to 99/10.

well, the denominator is already 10, so we don't need any transformation.

but if we had not seen that and went for 20 as desired denominator, we would have had to multiply by 2/2 giving us

198/20.

so, for the final sum :

15/10 + 99/10 = 114/10 = 57/5

and in case of 1/20th :

30/20 + 198/20 = 228/20 = 114/10 = 57/5

now, should that original problem have been

1/5 + 9/9 ?

the same principles apply.

bring both fractions to the same denominator.

9/9 = 1

and that can be transformed easily into any other denominator expression - like 5/5.

and then we have

1/5 + 5/5 = 6/5

but if we had not seen that simple approach, we could have turned both into fractions with denominator 5×9 = 45.

9/45 + 45/45 = 54/45 = 6/5

Answer:

m = 5 and c = -2

Step-by-step explanation:

[tex]let \: y = \sqrt{20} \times {10}^{ - 3} \times {10}^{5x} \\ be \: equation \: 1[/tex]

Now

[tex]y = \sqrt{5} ( \sqrt{20} \times {10}^{ - 3} \times {10}^{5x} ) \\ y = \sqrt{100} \times {10}^{ - 3} \times {10}^{5x} \\ y = 10 \times {10}^{ - 3} \times {10}^{5x} [/tex]

[tex]using \: rules \: of \: indices \: we \: get \\ y = {10}^{1 - 3 + 5x} \\ y = {10}^{ - 2 + 5x} \\ [/tex]

[tex]now \: take \: log \: of \: both \: sides \: and \: use \: laws \: of \: logarithm \\ we \: get \\ [/tex]

[tex] log(y) = log( {10}^{ - 2 + 5x} ) \\ log(y) = ( - 2 + 5x) log(10) \\ log(y) = - 2 + 5x \\ log(y) - 5x = - 2 \\ \\ comparing \: this \: to \: \\ log(y) - mx = c \\ \\ we \: get \: m \: = 5 \: and \: c = - 2[/tex]

Answer:

3 acres

Step-by-step explanation:

If the farmer plants 4 1/2 acres in one full year, to figure out how much is planted if the year is 2/3 over, just do:

= [tex]\frac{2}{3}[/tex] [tex]of[/tex] [tex]4\frac{1}{2}[/tex]

= [tex]\frac{2}{3} * 4 \frac{1}{2}[/tex]

= [tex]\frac{2}{3} * \frac{9}{2}[/tex]

= [tex]3[/tex]

This means that 3 acres are planted

The number of acres that were planted by the farmer if the year is 2/3 will be 3.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

A farmer plants the same amount every day, adding up to 4 1/2 acres at the end of the year. If the year is 2/3 over.

Then the number of the acre will be

[tex]\rightarrow (4 +\dfrac{1}{2}) \times \dfrac{2}{3}\\\\\rightarrow \dfrac{9}{2} \times \dfrac{2}{3}\\\\\rightarrow 3[/tex]

More about the multiplication link is given below.

https://brainly.com/question/19943359

Answer:

201, 206, 216, 228, 240

Step-by-step explanation:

Answer:

the last one

Step-by-step explanation:

The two on the right bounce up and down around -1. Two up and two down from -1. But only the one on the bottom right takes 3 pi to come back to the same place it started.

Explanation:

[tex]\displaystyle y = 2cos\:(\frac{2}{3}x - \frac{\pi}{2}) - 1 \\ y = 2sin\:\frac{2}{3}x - 1 \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{3}{4}\pi} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{2}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\pi} \hookrightarrow \frac{2}{\frac{2}{3}}\pi \\ Amplitude \hookrightarrow 2[/tex]

OR

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\pi} \hookrightarrow \frac{2}{\frac{2}{3}}\pi \\ Amplitude \hookrightarrow 2[/tex]

You will need the above information to help you interpret the graph. So, first off, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-4\frac{1}{2}\pi, -1],[/tex] from there to [tex]\displaystyle [-1\frac{1}{2}\pi, -1],[/tex] they are obviously [tex]\displaystyle 3\pi\:units[/tex] apart, telling you that the period of the graph is [tex]\displaystyle 3\pi.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = -1,[/tex] in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

*If you wanted to know the equation(s) of the graph, look above. If you have any questions on how the equation(s) came about, do not hesitate to ask.

I am delighted to assist you at any time.

6 It is divisible by 2 and by 3.

4 it is divisible by 4...

The divisibility rules of 4 and 6 are completely different. In the divisibility rule of 4, if the last two digits are zeros or the number formed by the last two digits is exactly divisible by 4, then we can say that a number is divisible by 4.

HOPE ITS HELPFUL FOR U MATE

Answer:

always

Step-by-step explanation:

they would all have the same gradient & be parallel to each other!

ie. A || B ,   B || C

in this case, A || C ^^

Answer:

always

Step-by-step explanation:

have the same gradient & be parallel to each other

Answer:

D. RWS and SWT

Step-by-step explanation:

Adjacent angles have a common side and a common vertex but they don't overlaps each other

The two angles that has these requirements are :

RWS and SWT

The two angles are said to be adjacent angles when they share the common vertex and side.

So , adjacent angles are :

Option D is the correct answer.

First, we can order the set in ascending order to get

76,77, 77, 78,79, 82, 82 ,84, 84, 87, 90, 95, 97, 100.

A stem-and-leaf plot has the tens digits on the left side, and the units digits on  the right side, so this set would look like

7   |   6, 7, 7, 8, 9

8   |   2, 2, 4, 4, 7

9   |   0, 5, 7

10  |   0

Answer:

H. 40 inches

Step-by-step explanation:

On Wednesday, he is 40 inches taller. ... That would make 5 days of growth, for 100 inches. But this is only 3 days therefore he would grow 40 inches taller

ω in terms of m and k is expressed as  [tex]\omega = \sqrt{\frac{k}{m} }[/tex]

The given expression is as follows;

     [tex]T_s = 2\pi \sqrt{\frac{m}{k} } , \ \ \\\\ T_s = \frac{2\pi}{\omega}[/tex]

To find:

From the given expression above make ω the subject of the formula;

[tex]T_s = \frac{2\pi}{\omega} = 2\pi \sqrt{\frac{m}{k} } \\\\ \frac{2\pi}{\omega} = 2\pi \sqrt{\frac{m}{k} }\\\\ \frac{2\pi}{\omega} = \sqrt{4\pi^2\frac{m}{k} }\\\\square \ both \ sides \ of \ the \ equation;\\\\(\frac{2\pi}{\omega})^2 = 4\pi^2\frac{m}{k} \\\\\frac{4\pi^2}{\omega^2}= \frac{4\pi^2m}{k} \\\\\omega^2 4\pi^2m = k4\pi^2 \\\\divide \ both \ side \ by \ 4\pi ^2 \\\\\omega^2 m = k\\\\divide \ both \ sides \ by \ m\\\\\omega^2 = \frac{k}{m} \\\\[/tex]

[tex]take \ the \ square \ root \ of \ both \ sides \ of \ the \ equation\\\\\omega = \sqrt{\frac{k}{m} }[/tex]

Therefore, ω in terms of m and k is expressed as [tex]\omega = \sqrt{\frac{k}{m} }[/tex]

To learn more about subject of formula visit: https://brainly.com/question/15469690

(i) The number of students who registered for political science is 150

(ii) The number of students who registered for political science and geography but not economics is 50

(iii) The number of students who registered for economics and political science but not geography is 20

The Venn diagram for the question is shown in the attachment below.

E represents Economics

G represents Geography

and P represents Political science

From the question,

10 for economics only, that is, n(E∩G'∩P') = 10

150 from economics and geography, that is n(E∩G) = 150

90 from economics but not political science, that is, n(E∩P') = 90

210 from geography, that is, n(G) = 210

120 from political science and geography, n(P∩G) = 120

180 from economics, that is, n(E) = 180

Total of student registered for courses is 250, that is, n(ξ) = 250

Now from the given information,

n(E∩G∩P') = n(E∩P') - n(E∩G'∩P') = 90 - 10 = 80

n(E∩G∩P) =  n(E∩G) - n(E∩G∩P') = 150 - 80 = 70

n(E∩P∩G') = n(E) - [n(E∩G'∩P') + n(E∩G∩P') + n(E∩G∩P)]

= 180 - [10+80+70] = 180 - 160 = 20

n(P∩G∩E') = n(P∩G) - n(E∩G∩P) = 120 - 70 = 50

n(G∩E'∩P') = n(G) - [n(E∩G∩P') + n(E∩G∩P) + n(P∩G∩E')]

= 210 -[80+70+50] = 210 - 200 = 10

All of these are shown in the Venn diagram

(i) To determine the number of students who registered for political science, we will first determine n(P∩G'∩E'), that is, those who registered for political science only.

Let n(P∩G'∩E') = x

Then, using the Venn diagram, we can write that

10 + 80 + 20 + 70 + 10 + 50 + x = n(ξ) = 250

240 + x = 250

x = 250 - 240

x = 10

n(P∩G'∩E') = 10

∴ 10 registered for political science only

Now, number of students who registered for political science n(P) is

n(P) = n(E∩P∩G') + n(E∩G∩P) +  n(P∩G∩E')  + n(P∩G'∩E')

n(P) = 20 + 70 + 50 + 10

n(P) = 150

∴ 150 students registered for political science

(ii) For the number of students who registered for political science and geography but not economics, that is, n(P∩G∩E')

As determined above and as shown in the Venn diagram,

n(P∩G∩E') = 50

∴ 50 students registered for political science and geography but not economics

(iii) For the number of students who registered for economics and political science but not geography​, that is, n(E∩P∩G')

As determine above and as shown in the Venn diagram as well

n(E∩P∩G') = 20

∴ 20 students registered for economics and political science but not geography​

Hence,

(i) The number of students who registered for political science is 150

(ii) The number of students who registered for political science and geography but not economics is 50

(iii) The number of students who registered for economics and political science but not geography is 20

Learn more here: https://brainly.com/question/15311191

sin O = 1/2 = p/h

p=1, h = 2.

by pythagoras tgeorem,

b =

[tex] \sqrt{3} [/tex]

tan0= p/b

[tex]1 \div \sqrt{3} [/tex]

9514 1404 393

Answer:

  no feasible solutions

Step-by-step explanation:

There are so many inequalities that determining the area covered by all 5 of them is problematic. Hence, we have reversed all of them in the attached graph, so any feasible solution region would remain white. Alas, there is no such region.

This system of inequalities has no feasible solution.

Answer:

6632.55

Step-by-step explanation:

P=A*(1+r/100)^x

P=6250*(1+2/100)^3

P=6632.55

Answer:

$6632.55

Step-by-step explanation:

→ Find the multiplier

( 100 + 2 ) ÷ 100 = 1.02

→ Multiply the investment by the multiplier to the power of years

6250 × ( 1.02 )³ = 6632.55

Answer:

x = 155º

Step-by-step explanation:

y = 25°    {Vertically opposite angles}

x + y = 180    {Co-interior angles are supplementary}

x + 25 = 180

Subtract 25 from both sides

x = 180 - 25

x = 155°

Answer:

x = -11/2

Step-by-step explanation:

The ratios need to stay the same

5x        11

----- = -------

x-2       3

Using cross products

5x*3 = (x-2) 11

15x = 11x - 22

Subtract 11 from each side

15x-11x = -22

4x = -22

x = -22/4

x = -11/2

Answer:

5 whole number 1/2

Step-by-step explanation:

5x:(x-2)=11:3

(:)This simply means ''ratio''

5x/(x-2) = 11/3

(cross multiply)

11(x-2) = 3(5x)

11x-22 = 15x

collect like terms

15x - 11x = 22

4x = 22

x = 22/4, but it is best you put it as a Mixed number.

x = 5 whole number 2/4, which can be reduced to

x = 5 whole number 1/2