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2 years ago

How many bases

formula"> are there such that $663_b$ is prime?

Mathematics

1 answer:

vivado [14]2 years ago

5 0

Answer:

none

Step-by-step explanation:

We assume you intend positive rational bases.

$663_b$ is divisible by 3, so cannot be prime.

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Two drivers, Alison and Kevin, are participating in a drag race. Beginning from a standing start, they each proceed with a const

Vilka [71]

Answer:

Alison wins against Kevin by 0.93 s

Step-by-step explanation:

Alison covers the last 1/4 of the distance in 3 seconds, at a constant acceleration $a_a$ , we have the following equation of motion

$s/4 = a_at_a^2/2$

where s (m) is the total distance, ta = 3 s is the time

$s = 4a_a3^2/2 = 18a_a$

$a_a = s/18$

Similarly, Kevin overs the last 1/3 of the distance in 4 seconds, at a constant acceleration $a_k$ , we have the following equation of motion:

$s/3 = a_kt_k^2/2$

tk = 4 s is the time

$s = 3a_k4^2/2 = 24a_k$

$a_k = s/24$

Since $a_a = s/18$ we can conclude that $a_a > a_k$ , so Alison would win.

The time it takes for Alison to cover the entire track

$s = a_aT_a^2/2$

$T_a^2 = 2s/a_a = 2s/(s/18) = 36$

$T_a = \sqrt{36} = 6 s$

The time it takes for Kevin to cover the entire track

$s = a_kT_k^2/2$

$T_k^2 = 2s/a_k = 2s/(s/24) = 48$

$T_a = \sqrt{48} = 6.93 s$

So Alison wins against Kevin by 6.93 - 6 = 0.93 s

4 0

1 year ago

A spinner is divided into 8 equal sections. lara spins the spinner 120 times. it lands on purple 30 times. how many more times d

kvv77 [185]

She should not spin the spinner any more times, the relative probability is already more than the theoretical probability.

If there is only 1 purple section out of 8, that gives purple a 12.5% chance of being spun.

However, Lara got purple 30 out of 120 times. That is 25%. She is already over.

How many of the sections were purple?

8 0

1 year ago

Which expression is equivalent to (x^6y^8)^3\x^2y^2

Damm [24]

Answer:

$\large\boxed{\dfrac{(x^6y^8)^3}{x^2y^2}=x^{16}y^{22}}$

Step-by-step explanation:

$\dfrac{(x^6y^8)^3}{x^2y^2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{(x^6)^3(y^8)^3}{x^2y^2}=\dfrac{x^{(6)(3)}y^{(8)(3)}}{x^2y^2}=\dfrac{x^{18}y^{24}}{x^2y^2}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=x^{18-2}y^{24-2}=x^{16}y^{22}$

5 0

2 years ago

Read 2 more answers

Lila needs a custom frame for a painting that her friend made for her. I’ve Been Framed is offering 50 percent off plus an addit

nikklg [1K]

Answer:

The location offering the better price is The Framers. It is cheaper by $1.35

Step-by-step explanation:

I've Been Framed:

50% of $115 = $57.5

10% of $57.5 = $5.75

$57.5 - $5.75 = $51.75

Total: $51.75

The Framers:

30% of $120 = $36

$120 - $36 = $84

40% of $84 = $33.6

$84 - $33.6 = $50.4

Difference: $1.35

7 0

1 year ago

3. A CD costs £9.50 in London and

adelina 88 [10]

Step-by-step explanation:

Only Q4 has clear details

therefore, solving Question 4,

1 euro = $1.17

then, €20.46 =20.46×1.17 = $23.93.

1 pound =1.28 dollars.

then, £12.60 = 12.60×1.28 =$16.128

therefore, MP3 in pound is cheaper in dollar by $7.81.

6 0

2 years ago