A high speed train travels a distance of 503 km in 3 hours.
The distance is measured correct to the nearest kilometre.
The time is measured correct to the nearest minute.
By considering bounds, work out the average speed, in km/minute, of the train to a suitable degree of accuracy.
You must show your working.
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:

A rational number is a number that can be expressed as a fraction (the ratio of two integers).  

Integer:  A whole number that can be positive, negative, or zero.

To calculate if each radical can be expressed as a rational number, convert the decimals into rational numbers, then simplify:

[tex]\sqrt{121}=\sqrt{11^2}=11=\dfrac{11}{1} \quad \leftarrow \textsf{rational}[/tex]

[tex]\sqrt{12.1}=\sqrt{\dfrac{1210}{100}}=\dfrac{\sqrt{1210}}{\sqrt{100}}=\dfrac{\sqrt{121\cdot 10}}{10}=\dfrac{\sqrt{121}\sqrt{10}}{10}=\dfrac{11\sqrt{10}}{10} \leftarrow \textsf{not rational}[/tex]

[tex]\sqrt{1.21}=\sqrt{\dfrac{121}{100}}=\dfrac{\sqrt{121}}{\sqrt{100}}=\dfrac{\sqrt{11^2}}{\sqrt{10^2}}=\dfrac{11}{10} \leftarrow \textsf{rational}[/tex]

[tex]\sqrt{0.0121}=\sqrt{\dfrac{121}{10000}}=\dfrac{\sqrt{121}}{\sqrt{10000}}=\dfrac{\sqrt{11^2}}{\sqrt{100^2}}=\dfrac{11}{100} \leftarrow \textsf{rational}[/tex]

Therefore, [tex]\sf \sqrt{12.1}[/tex] is not a rational number.

[tex]\huge\sf\underline{Answer} [/tex]

[tex]\sf\longrightarrow selling \: prize \: = \frac{100 + profit\%}{100} \times cp[/tex]

[tex]\sf\longrightarrow \frac{108}{100} \times 15000 = 16200[/tex]

Let the marked prize of the TV be x .

[tex]\sf\longrightarrow discount = 20\% \: of \: x \: = \frac{20}{100}x = \frac{x}{5} [/tex]

We have SP = MP - Discount

[tex]\sf\longrightarrow 16200 \: = \: x - \frac{x}{5} [/tex]

[tex]\sf\longrightarrow 16200 \: = \frac{4x}{5} [/tex]

[tex]\sf\longrightarrow x \: = \: 20250[/tex]

Hence , The marked prize of the TV is ₹20,250 .

Hope it helps ~

Answer:

see below

Step-by-step explanation:

1 9/12 = > 1 3/4

........

The circumference of the circle is 75.36 cm.

Diameter of the circle is 24 cm,

[tex]\pi = 3.14[/tex]

Circumference of the circle is [tex]2\pi r[/tex].

So, Radius, r = 24/2 = 12 cm.

Now, Putting the value in the above formula, we get

2 × 3.14 ×12 = 3.14 × 24 = 75.36 cm.

Hence, the circumference of the circle is 75.36 cm.

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Answer:

Here is the ans ...hope it helps:)

Answer:

300:288

Step-by-step explanation:

5+2=7

280 /7 = 4

20:8

300:288

i can, first add then take away and u done!

Step-by-step explanation:

Answer: 2,444

Step-by-step explanation: We can find the answer to this problem by simplifying the scientific notation, and then adding. You would end up with 2,000 + 400 + 40 + 4 if done correctly. Hope this helps!

Answer:

9

Step-by-step explanation:

Vertical lines are parallel so the given interior angles are supplementary and their sum is equal to 180:

4x + 9 + 16x - 9 = 180 add like terms

20x = 180 divide both sides by 20

x = 9

The value of x for which the lines m and l are parallel is 31 degrees

The given diagram includes two parallel lines m and l, since the line are parallel hence the sum of the angles 105 and 3x - 18 are supplementary that is;

105 + 3x - 18 = 180

Simplify for the value of x

87 + 3x = 180

3x = 180 - 87

3x = 93

x = 93/3

x = 31

Hence the value of x for which the lines m and l are parallel is 31 degrees

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Answer:

  a. $0.47 per ounce

  b. $0.36 per ounce

  c. the gallon size costs less per ounce

Step-by-step explanation:

A unit rate is a rate that is expressed with one unit in the denominator. That is, it is <some amount> per unit. The <some amount> value will generally depend on what unit is chosen. This problem suggests the desired unit is 1 oz of paint.

__

Unit cost for a quart:

  ratio = cost/ounces = $14.99/(32 oz) ≈ $0.468/oz ≈ $0.47/oz

__

Unit cost for a gallon:

  ratio = cost/ounces = $45.99/(120 oz) ≈ $0.359/oz ≈ $0.36/oz

__

The cost per ounce is less for the gallon size. If at least 3 quarts of paint is needed, then buying it in the gallon size will cost less.

If less than 3 quarts are needed, then a gallon container will cost more than is necessary for the paint required. The "better deal" depends on the amount of paint required.

Collin's sampling method will better represent the entire population.

Determine which sampling method will better represent the entire population.

From the question, we understand the Collin selected random names from the school directory.

While Karl surveyed only the students sitting close to him.

Karl's method is biased because students sitting far from him do not have a chance of being surveyed.

Hence, Collin's sampling method will better represent the entire population.

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Answer:

[tex]41^{\circ}[/tex]

Step-by-step explanation:

[tex]~~~~~~\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\\\\\implies \cos \theta = \dfrac{9}{12}\\\\\\\implies \theta = \cos^{-1} \left( \dfrac 9{12} \right)\\\\\\\implies \theta \approx 41^{\circ}[/tex]

Answer:

41°

Step-by-step explanation:

Since the adjacent side and the hypotenuse are given, let's take the cosine ratio of the missing angle.

cos θ = adjacent side / hypotenuse

===========================================================

Given :

⇒ Adjacent side = 9

⇒ Hypotenuse = 12

===========================================================

Solving :

⇒ cos θ = 9/12

⇒ cos θ = 0.75

⇒ θ = cos⁻¹ (0.75)

⇒ θ = 41.4096221....

⇒ θ = 41° (to the nearest degree)

Answer:

So the two numbers are {15, 25}.

Step-by-step explanation:

Simultaneous Equations:

xy = 375

x = y + 10

Subsitute the Second One into the First:

(y + 10)y = 375

y^2 + 10y - 375 = 0

y = 15 [and not -25 (natural numbers are not negative)]

Solve for x by Substituing y in the Second Equation:

x = 15 + 10

x = 25

Solution:

So the two numbers are {15, 25}.

Answer:

  15 and 25

Step-by-step explanation:

The given relations between the two numbers allow you to write a system of equations. Algebraic solution of the system involves the solution of a quadratic equation. The numbers are "natural numbers", so are both positive integers.

__

Let x and y represent the smaller and larger of the two numbers, respectively. The given relations are ...

  y = x +10 . . . . . . the larger is 10 more than the smaller

  xy = 375 . . . . . . their product is 375

Substituting for y in the second equation, we have ...

  x(x +10) = 375

Adding (10/2)² will complete the square.

  x² +10x +25 = 375 +25 . . . . add 25

  (x +5)² = 400 . . . . . . . . . . . write as a square

  x +5 = √400 = 20 . . . . . . positive square root

  x = 20 -5 = 15

  y = x +10 = 25

Those two numbers are 15 and 25.
__

The attachment shows a graphical solution of the equations.

_____

Additional comment

Your number sense tells you that both numbers end in 5. Their geometric mean is √375 ≈ 19.4, so the first numbers that deserve consideration are numbers ending in 5 that are either side of this value: 15 and 25.

You can also consider their arithmetic mean. If that is represented by z, then we have (z-5)(z+5)=375  ⇒  z²-25=375  ⇒  z²=400  ⇒  z=20, and the two numbers are 20±5.

Answer:

see the attachment photo!

The different ways Johnny can improve his meal is 16

We can use combinations for this case,

Total number of distinguishable things is m.

Out of those m things, k things are to be chosen such that their order doesn't matter.

This can be done in total of

[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex]  ways.

If the order matters, then each of those choice of k distinct items would be permuted k! times.

So, total number of choices in that case would be:

[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]

This is called permutation of k items chosen out of m items (all distinct).

Given;

Mother tells him he may only make two additions to his meal

First addition; 1C4

Second addition; 1C4

1C4=4

=4x4

=16

Therefore, by combinations and permutations their will be 16ways

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Answer:

45 becasue it has to be over 43

Step-by-step explanation:

The test score of the student who joined the class will be;

⇒ 55

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 mean test score of 12 students = 42

And, A student joins the class and the mean becomes 43.

Now,

Total score for 12 students is,

⇒ x / 12 = 42

⇒ x = 42 × 12

⇒ x = 504

Here, A student joins the class and the mean becomes 43.

Let the student who join = y

So, We get;

⇒ (504 + y) / 13 = 43

⇒ 504 + y = 43×  13

⇒ 504 + y = 559

⇒ y = 559 - 504

⇒ y = 55

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Answer:

Discount amount = 34

Step-by-step explanation:

Discount amount = 202 - 168 = 34

Step-by-step explanation:

here, given points are

(-2,-1),(-5,-3),(-5,-4)

now

(X,y)________ (-y,X)

(-2,-1)________ (1,-2)

(-5,-3)________ (3,-5)

(-5,-4)________ (4,-5)

now plot the points in the graphs

Answer:

36

Step-by-step explanation:

Question:

[tex] \bigg(\cfrac{10}{2} \bigg)\times 7 + 5 - 4[/tex]

Solution:

Here, we need to use PEMDAS rule, where:

There's a rule as well, the sum given is need to solved from the left, whichever sign is there.

Solved:

[tex]\bigg(\cfrac{10}{2} \bigg)\times 7 + 5 - 4[/tex]

Solve for parentheses first:

[tex] = 5 \times 7 + 5 - 4[/tex]

Then multiplication of course:

[tex] = 35 + 5 - 4[/tex]

Then addition:

[tex] = 4 0 - 4[/tex]

[tex] =36[/tex]

Hence, the answer is 36.

The number of walkways that must be shoveled to result in equal billing from both companies is 10

From the question, we are to determine how many walkways must be shoveled to result in equal billing from both companies

Let the number of walkways be x

From the given information,

Bobs snowplow business charges 300$ per season plus 10$ for each walkway shoveled

∴ If x walkways are shoveled

the billing will be $300 + $10x

For Mikes snow removal

Mikes snow removal charges 250$ per season plus 15$ per walkway

∴ If x walkways are shoveled

the billing will be $250 + $15x

Now, we are to determine the value of x for which the billings from both companies will be equal,
That is,

$300 + $10x = $250 + $15x

$15x - $10x = $300 - $250

$5x = $50

x = $50 / $5

x = 10

Hence, the number of walkways that must be shoveled to result in equal billing from both companies is 10.

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Answer:

2/7  ?

Step-by-step explanation:

Because 1/4 divided by 7/8th is 1/4. Hope this works

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &175\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ t=years\dotfill &10\\ \end{cases} \\\\\\ A=175(1 + 0.12)^{10}\implies A=175(1.12)^{10}\implies A\approx 543.52[/tex]

The characteristics I notice in top 3 mobile banking vs. online banking. is that:

They are:

The top 3 banking activities done via online banking are:

Therefore, the characteristics I notice in top 3 mobile banking vs. online banking. is that:

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The probability that the book is nonfiction given that it is hard-covered is 4/11

From the complete question, we have:

Total = 20

n(H ∩ N) = 4

n(H) = 11

This means that:

P(H ∩ N) = n(H ∩ N)/Total

So, we have:

P(H ∩ N) = 4/20

The conditional probability is then calculated using:

P(N | H) =4/20 ÷ 11/20

Evaluate

P(N | H) = 4/11

Hence, the probability that the book is nonfiction given that it is hard-covered is 4/11

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Answer:

Step-by-step explanation:

4/20

11/20

4/11

yw :)

Step-by-step explanation:

a rhombus is a parallelogram with 4 identical sides.

it has therefore two pairs of equal angles.

as any quadrilateral the sum of all interior angles is 360°.

(and yes, as add-on, the diagonals bisect each other at right angles).

so, one interior angle is 79°.

that means it has a twin that is also 79°.

together they have 79×2 = 158°.

that leaves

360 - 158 = 202°

for the other 2 angles (they must be equal too).

so, each of them has

202/2 = 101°

so, the other 3 angles are

79°, 101°, 101°

The value of x is 6.

Complementary angles are angles that sum up to 90°.

Analysis:

For angles A and B, to be complementary, the sine of angle A  must be equal to the cosine of angle B.

sin A = cos B

5X+9 = 3x+21

5x - 3x = 21 - 9

2x = 12

x = 6

In conclusion, the value of x to make angles A and B complementary is 6.

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Answer:

after 25 months both options cost $2000

Step-by-step explanation:

the options are the same at the point of intersection of the 2 lines

the lines intersect at (25, 2000)

That is after 25 months both options will cost $2000

Answer:

Please don't hesitate to give a "thumbs up" for the answer in case the answer has helped you 1. 2 M, 2R, 2 P are placed in shelf randomly P(similar a…

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Transcribed image text: Your Turn Find the probability using permutation with repetition 1. There are 2 mystery books, 2 romance books, 2 poetry books to be randomly placed on a shelf. What is the probability that the mystery books are next to each other, the romance books are next to each other, and the poetry books are next to each other? (For example, MMRRPP). 2. The school jazz band has 4 boys and 4 girls, and are randomly lined up for a yearbook photo. Find the probability of getting all of the boys grouped together.

Step-by-step explanation:

CORRECT ME IF IM WRONG

[tex]|\Omega|=1+2+3+3=9\\|A|=3\\\\P(A)=\dfrac{3}{9}=\dfrac{1}{3}\approx33,3\%[/tex]

Check the picture below.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+52}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 52}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (52)^2}{4(-16)}\right) \implies \left( - \cfrac{ 52 }{ -32 }~~,~~0 - \cfrac{ 2704 }{ -64 } \right)[/tex]

[tex]\left( \cfrac{13}{8}~~,~~\cfrac{169}{4} \right)\implies \underset{\stackrel{\uparrow \hspace{3em}}{seconds\qquad }}{\stackrel{\stackrel{\qquad feet}{\hspace{3em}\downarrow }}{\left( 1\frac{5}{8}~~,~~42\frac{1}{4} \right)}}[/tex]