1. When Aaron runs the 400 meter dash, his finishing times are normally distributed with a mean of 80 seconds and a standard deviation of 2.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 99.7% of his finishing times in the 400 meter race.
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Given:

The two sides of a triangle are 2 and 6.

To find:

The side length that would NOT work to make a triangle with the two slide lengths of 2 and 6.

Solution:

For a triangle, the sum of two smaller sides must be greater than the largest side.

Let x be the third side.

Case 1: x is the largest side, then

[tex]2+6>x[/tex]

[tex]8>x[/tex]              ...(i)

Case 2: x is not the largest side, then

[tex]2+x>6[/tex]

[tex]x>6-2[/tex]

[tex]x>4[/tex]              ...(ii)

From (i) and (ii), we get

[tex]4<x<8[/tex]

Here, 4 and 8 are not included.

6, 5, 7 are included in the above interval, but 4 is not included in the above interval. It means 4 would NOT work to make a triangle with the two slide lengths of 2 and 6.

Therefore, the correct option is D.

Answer: So we'll use trig to solve this because it's a right triangle. The hypotenuse is the ladder (h) and the two smaller sides are the ground and the vertical wall (w).

That angle ladder makes with the ground = €

SOH: sin € = opposite/hypotenuse

No the ladder won't be safe!!!

Now let's make it safe:

The ladder's length (w) is constant, so stays 12

So now let's ask in an inequality what height will be safe (75° or less)

what does that mean?? well as long as you put the ladder against the wall so that the height from ground to top of the ladder is < 11.6 ft!!

Hope that helps! :-D

Step-by-step explanation:

Answer:

43.75 or simplified as 43 3/4 which is a mixed number

Step-by-step explanation:

How I did it is divide 5 and 8 and got 0.625 and I divided 70 by 0.625 and got 43.75 and I simplified it as a maxed number and got 43 3/4

Answer:

im not sure but i think its -25

Step-by-step explanation:

hope im not wrong:)

hope you have a great day and god loves you:))

Answer: -30

Step-by-step explanation:

Answer:

The amount Sandy earns from babysitting is proportional to the number of hours she works. The graph represents this proportional relationship.

Step-by-step explanation:

Answer:

The student explains that the ordered pair (0, 0) means that when Sandy

babysits for zero hours, she earns zero dollars

Step-by-step explanation:

Answer: reasons to love yourself, plus how self-love can change your life. ... We don't always have a warm body to hold us in a hard moment. ... counterintuitive—claiming that the best way to change yourself is to accept yourself.

Step-by-step explanation:

Answer:

Because we are perfect just the way we are. What we think of ourselves is much more important than what other people think of us. Not to mention that there is literally no reason for someone to try to shame you about something unless they are jealous of you for one reason or another.

Answer:

(From left to right)

y = -13; -12; -3; -1; and 1

Step-by-step explanation:

Answer:

43%

Step-by-step explanation:

Orinally the decimal percentage is 43.1034% so we just round to 43%

Answer:

43.1`

Step-by-step explanation:

my friend helped me :)

Answer:

its 7.5 pi

Step-by-step explanation:

The length of the arc of the particle circle is equal to  23.55 units

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here the radius of the circle as 5 units thus the length of the arc which makes an angle of π-π/2=3π/2 is angle subtended at the centre times the radius of the circle

Arc length = 5×3π/2

                  = 15π/2

                  = 15×3.14 /2

                  = 23.55 units

Hence The length of the arc of the particle circle is equal to  23.55 units

Learn more about circumference of the circle here:

https://brainly.com/question/14200825

#SPJ2

Answer:

i think 1996 but i don't know if your adding subtracting but i add and i got 1996

Answer:

8. V≈471.2

9. 2513.3

Step-by-step explanation:

8. V=πr2h=π·52·6≈471.2389

9. V=πr2h=π·82·12.5≈2513.27412

Answer:

c

Step-by-step explanation:

Answer:

reflection across x=1 if I'm wrong sorry I cant see the screen well

Answer:

bces

Step-by-step explanation:

length:30ft

Step-by-step explanation:

if the perimeter is 100 than 20+20+x+x=100.

20+20=40

100-40=60

since there are two length sides, divide 60 by two and then you have your answer.

20+20+30+30=100

hope this helped

Answer:

8 gram

Step-by-step explanation:

It honestly depends on the yield, purity and other factors but I'm assuming the mass is conserved since no other variables were given

Answer:

the number is 5

Step-by-step explanation:

((n x 5 + 3.5) ÷ 2) -7.6 = 6.65

( 5n + 3.5) ÷ 2 = 14.25

5n + 3.5 = 28.5

5n = 25

n = 5

Answer:

[tex]\displaystyle x=\left\{\frac{\pi}{6}+2n\pi, \frac{5\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi\right\}, n\in\mathbb{Z}[/tex]

Step-by-step explanation:

We are given the equation:

[tex]2\cos^2(x)=\sin(x)+1[/tex]

And we want to find all solutions for x.

First, we should put the equation into terms of only one trigonometric ratio.

Since we are given cos²(x), we can turn this into sine. Recall the Pythagorean Identity which states:

[tex]\sin^2(x)+\cos^2(x)=1[/tex]

Therefore:

[tex]\cos^2(x)=1-\sin^2(x)[/tex]

By substitution:

[tex]2(1-\sin^2(x))=\sin(x)+1[/tex]

Distribute:

[tex]2-2\sin^2(x)=\sin(x)+1[/tex]

Isolate the equation:

[tex]2\sin^2(x)+\sin(x)-1=0[/tex]

We can factor:

[tex](2\sin(x)-1)(\sin(x)+1)=0[/tex]

Zero Product Property:

[tex]2\sin(x)-1=0\text{ or } \sin(x)+1=0[/tex]

Solve for each case:

[tex]\displaystyle \sin(x)=\frac{1}{2}\text{ or } \sin(x)=-1[/tex]

We can use the unit circle.

sin(x) = 1/2 for every π/6 and 5π/6. So, it will continue every 2π.

sin(x) = -1 every 3π/2. And this will also continue every 2π.

Hence, our solutions are:

[tex]\displaystyle x=\left\{\frac{\pi}{6}+2n\pi, \frac{5\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi\right\}, n\in\mathbb{Z}[/tex]

Note:

If you only need the solutions within the interval [0, 2π), then it is:

[tex]\displaystyle x=\left\{\frac{\pi}{6}, \frac{5\pi}{6}, \frac{3\pi}{2}\right\}[/tex]

Step-by-step explanation:

domain is all real positive numbers. x> 0

range is y>= -1

The x variable is for the number of books she buys to read so when x is 0!the cost would be what she paid for the reader.

The answer is B. The cost of the reader

Answer:

i think is either the first one or the last one.

i think it's one of those

Step-by-step explanation:

Answer: -2

x=-G-1= -2

4log(2)

Step-by-step explanation:

Answer:

median 1=41

median 2=73

Answer:

1: Mean: 53. Median: 48. Mode: There is no mode. Range: 84.

2: Mean: 57. Median: 52. Mode: No mode. Range: 63.

Hope this Helped!

Answer:

9/16

Step-by-step explanation:

Multiply across -

3*3 = 9

4*4 = 16

9/16

Answer:

Q1 --> 17

Q2 --> 20

Q3 --> 22.5

Interquartile

Range IQR 5.5

Step-by-step explanation:

Step 1

We rearrange the given data set

10, 16, 18, 20, 20, 21, 24, 25

Q2 (median):

Q1:

Q3:

Interquartile Range (IQR): Q3-Q1 -

Answer: 0.75

Step-by-step explanation:

3.75/5 = 0.75$

Answer:

4) The error made was that you were supposed to multiply 5 and 2. The answer is supposed to be 43.

5) B) 18

6) 18

7) B) 20

8) B) 28

Step-by-step explanation:

4)

36 - 3 + 5 · 2

36 - 3 + 10

43

5)

3(7) - 3 = 18

6)

3(2) + 2(4) + 4 =

6 + 8 + 4 =

18

7)

24 ÷ 3 + 12 = 8 + 12 = 20

8)

5(6) - 2 = 30 - 2 = 28

Answer:

jhgsdfgtyhujwert

Step-by-step explanation:

Answer:

Hexagon and rectangle

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

number of sides = (sum of interior angles / 180) + 2

(540 / 180) + 2 = 5