Hi please help this is due today thank u so much.

How many arrangements can be made using 2 letters of the word HYPERBOLAS if no letter is to be used more than once?

alisha [4.7K]

Answer:

90 arrangements

Step-by-step explanation:

Since there are no repititions of letters, there are unique 10 letters in total.

THe number of arrangements would be 2 permutation 10. We need the formula for permutation. That is:

$nPr=\frac{n!}{(n-r)!}\\$

Now, n = 10 [total] and r is 2, so we have:

$nPr=\frac{n!}{(n-r)!}\\\\_{10}P_{2}=\frac{10!}{(10-2)!}\\=\frac{10!}{8!}\\=\frac{10*9*8!}{8!}\\=10*9\\=90$

So, there can be 90 arrangements

3 0

4 years ago

What is the length of the segment with endpoints (-3, 4) and (5, 4)? A) 2 B) 8 C) 16 D) 64 E) 2 17

Cerrena [4.2K]

Answer:

The correct answer is B) 8

Step-by-step explanation:

$\sqrt{(4-4)^{2}+(5+3)^{2} } \\\\\\\sqrt{8^{2} } \\\\8$

8 0

3 years ago

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I did 3 over 7 then 8 over x. I'm getting decimals. ‍♀️

julia-pushkina [17]

Answer:

The length of side b is 9.

Step-by-step explanation:

Triangles are similar if they have the same shape, but can be different sizes.

When two figures are similar, the ratios of the lengths of their corresponding sides are equal.

If you know that two objects are similar, you can use proportions and cross products to find the length of an unknown side. We know that the triangle $ABC$ is similar to the triangle $XYZ$ . Therefore the following relation must be true:

$\frac{AB}{AC} =\frac{XY}{XZ}$

We know that side $AB$ is equal to 8, side $AC$ is equal to b, side $XY$ is equal to $2\frac{2}{3}$ , and side $XZ$ is equal to 3.

Substituting these values into the above relation and solving for b we get that:

$\frac{8}{b} =\frac{2\frac{2}{3} }{3}\\\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{2}{3}=\frac{8}{3}\\\\\frac{8}{b}=\frac{\frac{8}{3}}{3}\\\\8\cdot \:3=b\frac{8}{3}\\\\24=b\frac{8}{3}\\\\8b=72\\\\b=9$

5 0

3 years ago

A bacterial culture starts with 400 bacteria and grows at a rate proportional to its size. After 2 hours there will be 800 bacte

kotykmax [81]

Answer:

P(t) = 400×2^(t/2)
6400
5.0

Step-by-step explanation:

The wording "a rate proportional to its size" is an indication that growth (or decay) is exponential.

1) For many problems involving exponential growth, I like to use the numbers given in the problem statement as follows.

population = (initial population) × (growth factor)^(t/(growth period))

where the "growth period" is the period of time in which the population is multiplied by the "growth factor".

Here, we're given ...

(initial population) = 400

(growth factor) = 800/400 = 2

(growth period) = 2 . . . . hours

So, our population function can be written as ...

P(t) = 400×2^(t/2)

__

2) Putting t=8 into the formula, we get ...

P(8) = 400×2^(8/2) = 400×16 = 6400

After 8 hours, the population will be 6400.

__

3) Fill in the given number and solve for t.

2270 = 400×2^(t/2)

2270/400 = 2^(t/2)

Taking logs, we have ...

log(227/40) = (t/2)log(2)

t = 2×log(227/40)/log(2) ≈ 5.009

After 5.0 hours, the population will reach 2270.

7 0

4 years ago

HELP ME PLEASE LOVE U GUYS <33

geniusboy [140]

Answer:

100 in square

Step-by-step explanation:

LSA of square based pyramid = 2×a×l

= 2×5×10

= 100 in square

3 0

4 years ago

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