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3 years ago

The track team wants to choose 2 people to be team captain and equipment manager.

Mathematics

1 answer:

elena55 [62]3 years ago

4 0

Answer:

Scientists hypothesized that several species of frogs called tiger frogs evolved from a recent common ancestor. The

hypothesis was based on fossil evidence and on physical similarities among living species. Which of the following

provides the best additional support for the scientists' hypothesis?

Tiger frogs live near each other and are all preyed upon by the same predator species.

Tiger frogs have similarities in their mitochondrial DNA that

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Please help with these. I will give you brainlist

ser-zykov [4K]

Answer:

Step-by-step explanation:

3. slope of CB = rise/run = 5/12 BF = 5 CF = 12

BF ⊥ DF

DB (seg of two farthest points) = √BF²+DF² = √5²+32² = √1049 = 32.4

4. f(x) = 2x² - 5x -3 vertex : A (h,k) for f(x) = ax² + bx +c

h = - b/2a = - (-5 / 4) = 5/4

f = f(h) = 2*(5/4)² - 5*(5/4) - 3 =25/8 - 25/4 -3 = -49/8

A (5/4 , - 49/8) i.e. (1.25 , - 6.13)

negative root: 2x² - 5x -3 = (2x+1) (x- 3) x = - 1/2 y = 0

B (- 1/2 , 0)

x coordinate of AB: 1/2 (1.25 + -0.5) = 0.375

5 0

3 years ago

Read 2 more answers

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$

Observe that, because $n \geq 2$ and is an integer,

$n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5$

In concusion, the statement is true if and only if n is a non negative integer such that $n\leq 77$

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute $(4n)^4- \sum^{n}_{i=0} (2i)^4$ for 77 and 78 you will obtain:

$(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064$

$(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992$

7 0

4 years ago

The area of a rectangle is 3,878 square centimeters. If the rectangle has a width of 14 centimeters, what is its length?

astra-53 [7]

Answer:

277 cm

Step-by-step explanation:

$A=l*w\\3,878=l*14\\l=\frac{3,878}{14} \\l=277$

7 0

3 years ago

HELP ASAP PLEASE!!!!! <br> what is the factorization of the polynomial below -x^2-2x+48

Veronika [31]

I HOPE IT WILL HELP YOU. I DID HOW I KNOW .

8 0

3 years ago

Solve the given inequality and SHOW YOUR WORK<br> -2x + 3 < 5

natita [175]

-2x<5-3

-2x<2

divide both sides by -2

x<-1

remember +/-=-

that's why it's a negative answer

4 0

3 years ago