When Damian runs the 400 meter dash, his finishing times are normally distributed
with a mean of 60 seconds and a standard deviation of 1 second. Using the empirical
rule, determine the interval of times that represents the middle 99.7% of his finishing
times in the 400 meter race.

Answer:

[tex]a=\frac{7}{3}[/tex]

Step-by-step explanation:

[tex]\frac{a-1}{a-3}=\frac{a+1}{a-4}[/tex]

[tex](a-1)(a-4)=(a-3)(a+1)[/tex]

[tex]a^2-5a+4=a^2-2a-3[/tex]

[tex]-5a+4=-2a-3[/tex]

[tex]-3a+4=-3[/tex]

[tex]-3a=-7[/tex]

[tex]a=\frac{7}{3}[/tex]

Answer:

a) (2x+3) (x+4)

b) (5x-3) (x-1)

c) (-2x-3) (x-3)

d) 3(x-1) (3x-8)

e) -2(3x+5) (x-2)

f)  h(4x-3) (3x-4)

g) -(x-3) (x+7)

h) (3x-2) (x+3)

i)  2(2x+1) (x-2)

j) (3h+2) (h-7)

Step-by-step explanation:

your welcome :)

Answer:

a)

(x+4)(2x+3)

b)

(x-2)(5x-3)

c)

(-x+3)(2x-3)

d)

3(x-1)(3x-8)

e)

2(-x+2)(3x+5)

f)

h(3x-4)(4x-3)

g)

(x+7)(-x+3)

h)

(x+3)(3x-2)

i)

2(x-2)(2x+1)

j)

(h-7)(3h+2)

Hope this helps!

Answer:

2 + 5 x a = 22

Step-by-step explanation:

Answer: 1260 books

Step-by-step explanation:

2/5=0.4

19000x0.4=7600

12500x0.4=5000

7600+5000=12600

1/10=0.1

12600x0.1 = 1260

/Answer:

1,260 books (or C)

Step-by-step explanation:

1. 2/5 of fiction (12,500) are out, so 5,000 are out

2. 2/5 of non-fiction (19,000) are out, so 7,600 are out

3. Total books checked out are 12,600

4. 1/10 of checked out books are due this week, so 1,260 books (10%)

Answer:

14° and 166°

Step-by-step explanation:

Ok, so a supplementary angle is 180°.

Let's say one angle is x and the other angle is x+152.

We know these angles add up to a supplementary angle (180°) so...

x+(x+152)=180

x+x+152=180

2x+152=180

2x=28

x=14

So now we know one angle is 14°, we also know the other angle is x+152, knowing that x=14 we can plug it in 14+152= 166° for the other angle.

Hope this helps :)

Answer:

∘g(x)=2x2−4x−3. And g∘f(x)=(2x−3)(2x−5)

Answer:

it will take about 15 weeks

Step-by-step explanation:

15% of 674 is about 101.

so, 1500 divided by 101 is about 15

hope this helps :)

Answer:

A' = (-4, 7)

B' = (3, 5)

C' = (1, 2)

Step-by-step explanation:

The question is asking you to translate the function by adding 4 to the x-value of each point and 2 to the y-value of each point.

I didn't double-check my math, but since the question is asking for an ordered pair, this should be correct.

Answer:

?????????????????????????

Check the picture below.

Answer:

Joel can do 20 math problems in 90 seconds

He can do 1 math problem in 90/20 = 4.5 seconds

Now, Joel can do 32 math problems in

4.5×32

= 144 seconds

= 2 minutes 24 seconds

Step-by-step explanation:

Here I used the unitary method to sovle the question

Answer:

q

Step-by-step explanation:

Answer:

a. 587

b. 543

Step-by-step explanation:

a. Mean = sum / number of numbers

To find the sum, we can add the numbers up.

432 + 543 + 348 + 788 + 823 = 2934

There are 5 numbers. Our mean is thus

2934/5 = 586.8, or 587 when rounding up. We round up because we have a .8 at the end, and 8 ≥ 5

b. To find the median, we first must order the numbers. The numbers ordered are this:

348 ,  432 , 543 , 788 , 823

To find the median, we can cross off one number on each side until we are left with one or two numbers.

348 ,  432 , 543 , 788 , 823

cross out one number from each endpoint

432 , 543 , 788

cross out one number from each endpoint

543

Answer:

45.05 seconds

Step-by-step explanation:

Use the formula: d = v[tex]i[/tex] t + [tex]\frac{1}{2}[/tex] a[tex]t^{2}[/tex]

d = distance      v[tex]i[/tex] = initial velocity (m/s)    

t = time (s)     a = acceleration (m/[tex]s^{2}[/tex])

m is meters and s is seconds. They are units of measurement so leave them be.

Assuming the object is simply dropped, the initial velocity is 0 since the object was not moving before it was dropped.

The distance is 725 feet, which is 220.98 meters.

The acceleration is 9.81m/[tex]s^{2}[/tex] since that is the acceleration of Earth's gravity, aka free fall.

Time is what we are trying to find so just leave it as the variable t.

So plug the values into the equation:

220.98m = (0)(t) + [tex]\frac{1}{2}[/tex] (9.81m/[tex]s^{2}[/tex])(t)

220.98m = (4.905m/[tex]s^{2}[/tex])(t)

45.0519877676s = t

t = 45.05s

Remember to pay attention to units because your answer will be wrong otherwise

Answer:

Step-by-step explanation:

looks to be a parabola, so use vertex mode (h, k) =  (-1, 2)

y = a(x - h)² + k

y = a(x + 1)² + 2

another point on the curve seems to be (1, 6)

6 = a(1 + 1)² + 2

     1 = a

y = (x + 1)² + 2

or expand for standard form y = ax² + bx + c

y = (x² + 2x + 1) + 2

y = x² + 2x + 3

Answer:

See image

Step-by-step explanation:

Let w=width

And let l=length

Perimeter is the distance all the way around the outside of the shape. Add up all the sides to find it.

Step-by-step explanation:

let the width of the rectangle=x

the length=x+2.3

Since perimeter=28.6

We know that perimeter of a rectangle is given by

P=2(l+w)

28.6=2(x+2.3+x)

28.6=2(2x+2.3)

28.6=4x+4.6

28.6-4.6=4x

4x=24

x=24/4=6

Therefore width is 6inches and length is 8.3inches

Answer:

54 X 68=3672

Step-by-step explanation:

Answer:

Bottom right

Explanation:

visualize both triangle connected to the middle rectangle, and that's a triangular prism

Answer: the answer is 3 3/4

Answer:

Slope is [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

Given:

[tex]f(x)=-3\sqrt{x}[/tex]

Find the derivative using the product rule:

[tex]f'(x)=\frac{d}{dx}(-3)*\sqrt{x}+-3*\frac{d}{dx}\sqrt{x}[/tex]

[tex]f'(x)=-3*\frac{1}{2\sqrt{x}}[/tex]

[tex]f'(x)=\frac{-3}{2\sqrt{x}}[/tex]

Plug in coordinates to find slope at that point:

[tex]f'(9)=\frac{-3}{2\sqrt{9}}=\frac{-3}{2(3)}=\frac{-3}{6}=-\frac{1}{2}[/tex]

Therefore, the slope of the equation at the point (9,-9) is [tex]-\frac{1}{2}[/tex].

Answer:

Step-by-step explanation:

f(x) = -3√x

f'(x) = -1.5/√x

f'(x) = -1.5/√9

f'(x) = -1.5/3

f'(x) = -0.5

Answer:

HOLA MATE HERE IS UR ANSWER:-

Step-by-step explanation:

Answer:

D.18

Step-by-step explanation:

6-x=-12

-x=-12-6

-x=-18   divide both sides by -1

x=18

Answer:

all the small nembers x

Step-by-step explanation:

Answer:

Step-by-step explanation:

each zero of the function will have a factor of (x - x₀)

h(x) = a(x + 3)(x + 2)(x - 1)

h(x) = a(x + 3)(x² + x - 2)

h(x) = a(x³ + 4x² + x - 6)

or the third option works if a = 1

however this equation gives us the points (0, -6) and (-1. -4), so "a" must be -2

h(x) = -2x³ - 8x² - 2x + 12

to fit ALL of the given points as it fits the three zeros and also h(0) and h(-1) so I guess that is why the given group is a partial set of solution sets

Answer:

120

Step-by-step explanation:

round 19.99 to 20 and do 20 times 6