A tunnel has a semicircular cross-section
and a diameter of 10 m. If the roof of a bus
just touches the roof of the tunnel when
the bus is 2 m from one side, how high is
the bus?

this question is from the IGCSE maths student book1, shape and space 2 for Edexcel ​

Answer:

Step-by-step explanation:

Answer:

see explanation below

Step-by-step explanation:

You have three pairs of shoes (white, brown, and black), and you have 6 pairs of pants ( brown,  blue, grey, white, sand, and  black)

We use the Fundamental Counting Principle to find the number of possible pant-shoe combinations:

3 * 6 = 18

then we can find the probability of wearing by random selection brown shoes with either blue or grey pants:

prob (brown shoes & blue pants) + prob (brown shoes & grey pants) =

= 1/18 + 1/18 = 2/18 = 1/9

Answer:

skewed left

Step-by-step explanation:

Answer:

The answer is 48

Step-by-step explanation:

160% is the same as 1.60

A percent of something means you have to multiply them together

1.60 times 30=48

Hope this helps!!

Answer:

A. 67.8%

Step-by-step explanation:

the total number of occurences are 202

Now the total number of occurencess for 4 and below are 137

So Heres the quickest way to do it: Divide 137 by 202 then multiply it by 100 being 100%

Then you would get 67.8, then well put the percent sign behind it.

Answer:

Its c

Step-by-step explanation:

Answer:

Both

Step-by-step explanation:

Khan

Both of their strategies completing the square and factoring the left-hand side would work.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given a quadratic equation x² + 8x = 2x - 8.

They both agreed that first subtract 2x and add 8 to both sides and rewrite the equation as

x² + 6x + 8 = 0.

Both of their strategies would work.

As x² + 6x + 9 = 1

(x + 3)² = 1.

x + 3 = ± 1

x = ± 1 - 3.

x = - 2 or - 4.

x² + 6x + 8 = 0.

x² + 4x + 2x + 8 = 0.

x(x + 4) + 2(x + 4) = 0.

(x + 4)(x + 2) = 0.

x = - 4 or x = - 2.

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Answer:

5

The value of y is also 5!

The value of pair (x,y) is (5,5)

Hopefully this helped! :D

-LavenderVye

Answer:

8

Step-by-step explanation:

3/4 = 6/8

Answer:

8 cause common can be like

Answer:

C.

Step-by-step explanation:

[tex]\left \{ {{2x+y=10,3} \atop {3x+y=14,8}} \right.[/tex]

[tex]\left \{ {{y=10,3-2x} \atop {y=14,8-3x}} \right.[/tex]

10,3-2x=14,8-3x

x=4,5 - one hamburger

y=1,3 - one milk shake

OR:

$14,8-$10,3=$4,5 - one hamburger

2*4,5+y=10,3

y=1,3 - one milk shake

2y=2,6

Answer:

C is the answer i think

Step-by-step explanation:

Answer:

first one is the answer to this

Step-by-step explanation:

Answer:

358 randomly selected air passengers must be surveyed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

Assume that a prior survey suggests that about 22​% of air passengers prefer an aisle seat.

This means that [tex]\pi = 0.22[/tex]

How many randomly selected air passengers must you​ survey?

We need a sample of n, and n is found for which [tex]M = 0.051[/tex]. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.051 = 2.327\sqrt{\frac{0.22*0.78}{n}}[/tex]

[tex]0.051\sqrt{n} = 2.327\sqrt{0.22*0.78}[/tex]

[tex]\sqrt{n} = \frac{2.327\sqrt{0.22*0.78}}{0.051}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.327\sqrt{0.22*0.78}}{0.051})^2[/tex]

[tex]n = 357.2[/tex]

Rounding up

358 randomly selected air passengers must be surveyed.

Answer:

Uh 7/24?

Step-by-step explanation:

Just doing this in my head fyi lol

Answer:

$45.90

Step-by-step explanation:

What 15% off means is 85% of the original price ($54). 85% is the same as 17/20. Multiply 17/20 by 54 (or multiply 3/20 by 54 and subtract that from 54) to get the sale price.

(17 * 54)/20 (Multiply 17 by 54)

918/20 (Reduce if needed)

459/10 (Divide 459 by 10)

45.9

The sale price of the comforter is $45.90.

The correct answer is C) 54.34°.

Answer:

There is a total of 10 sausages. I am 100% sure.

Step-by-step explanation:

A bucket of sausages fed 15 hungry kittens. Each sausage or half of a sausage is sliced into two pieces. They chopped 20 sausages and gave each kitten two (perhaps unequal) portions.  Therefore, there were 34,952 sausages in the bucket.

At the start, there is one sausage bucket, and the 15 kittens want to share it.

The first cut divides the sausage into two pieces.

After the second cut, there are four pieces of sausage.

After the third cut, there are eight pieces.

After the fourth cut, there are 16 pieces.

As we can observe, the number of pieces of sausage doubles with each cut. After 20 cuts, there will be 2²⁰ (2 raised to the power of 20) pieces of sausage.

Now, since each kitten received two pieces of sausage, the total number of sausages in the bucket can be calculated by dividing the total number of pieces by 2 × 15 (since there are 15 kittens).

Total sausages = (2²⁰) / (2 × 15)

Let's simplify this:

Total sausages = 2¹⁹ / 15

Now, let's calculate the value:

Total sausages = 524,288 / 15

Total sausages = 34,952.53

Since you can't have a fraction of a sausage, we need to round down to the nearest whole number.

Therefore, there were 34,952 sausages in the bucket.

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Step-by-step explanation:

1 litre = 1000ml

780ml left

lost amount = 1000 - 780 = 220ml

9514 1404 393

Answer:

  mm:ss = 11:40

Step-by-step explanation:

We assume the amount of gain is proportional to the time that passes.

  g/7 = 5/3

  g = 7(5/3) = 35/3 = 11 2/3 . . . . minutes

The clock will have gained 11 minutes and 40 seconds after 7 days.

Let's solve your equation step-by-step.

x3+5x2+2x+10=0

Step 1: Factor left side of equation.

(x+5)(x2+2)=0

Step 2: Set factors equal to 0.

x+5=0 or x2+2=0

x=−5

Answer:

x=−5

Answer:

Part A 225-81=144

Step-by-step explanation:

1. 15×15 =225

2. 3×3×3×3 =81

Answer:

√10/2x

Step-by-step explanation:

Multiply by √6 on the top and bottom to rationalize the denominator.

(√15×√6)/(√6x×√6) = √90/6x = (√9×√10)/6x = 3√10/6x = √10/2x

Answer:

234

Step-by-step explanation:

So what we know is that

5x+9x= students

This equation is saying that for every 5 boys there are 9 girls

we can then plug in 364 for the number of students and add like terms

This means that 14x=364

this means that x=26

This means that there are 26 sets of 5 boys and 9 girls

this means that there are

130 boys

234 girls

Answer:

y=16

Step-by-step explanation:

x=2

y=-3x+22

y=-3(2)+22 then y=-6+22, y=16