When Caroline runs the 400 meter dash, her finishing times are normally distributed with a mean of 68 seconds and a standard deviation of 1.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 99.7% of her finishing times in the 400 meter race.

Answer:

It is a rational number.

Step-by-step explanation:

Rational numbers can be represented as a ratio/fraction. So whole numbers are rational with a denominator of 1.

This number can be written as 177/100. It is rational.

Should be 6^3.

Have a good day!

Answer:

x > 9.

Step-by-step explanation:

Here it is just simplifying the inequality.

6 - 2/3x < x - 9

Add 2/3x to both sides.

6 < 5/3x - 9

Add 9 to both sides.

15 < 5/3x

Multiply by 3/5.

9 < x

Flip it.

x > 9.

Answer:

x > 9

Step-by-step explanation:

I think I think I think I think

Answer:

1,920 words

Step-by-step explanation:

60 divided by 4 is 15

15 times 128 is 1,920.

Hope it helps! :)

Answer:

1920

Step-by-step explanation:

We know that it takes her 4 minutes to type 128 words

So we need to figure out how many it takes her to type a word per minute

128 divided by 4=32

So multiply 32 word by 60 ( 60 mins = an hour)

Answer=1920

Answer:

18

Step-by-step explanation:

Intersecting Secants Theorem:

6(x + 6) = 8(8 + 10)

6x + 36 = 8(18)

6x + 36 = 144

6x = 144 - 36

6x = 108

x = 18

Answer:

See Explanation

Step-by-step explanation:

Given

See attachment for complete question

First, we determine the cost function for all the three rides.

Ride A

From the graph, we have the following points

[tex](x_1,y_1) = (0,8)[/tex]

[tex](x_2,y_2) = (2,12)[/tex]

Calculate slope

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{12-8}{2-0}[/tex]

[tex]m = \frac{4}{2}[/tex]

[tex]m =2[/tex] --- This represents the rate per ride

The equation is the calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

So, we have:

[tex]y = 2(x - 0) + 8[/tex]

[tex]y = 2(x) + 8[/tex]

[tex]y = 2x + 8[/tex]

So, the cost function is:

[tex]C(x) =2x + 8[/tex]

Calculate the cost of admission i.e. x=0

[tex]C(0) = 2*0+8 = 8[/tex]

So, we have:

[tex]C(0) = 8[/tex] --- Admission Charge

[tex]C(x) =2x + 8[/tex] --- Cost function

[tex]m =2[/tex] --- Rate per ride

Ride B

From the table, we have the following points

[tex](x_1,y_1) = (0,12)[/tex]

[tex](x_2,y_2) = (4,15)[/tex]

Calculate slope

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{15-12}{4-0}[/tex]

[tex]m = \frac{3}{4}[/tex]

[tex]m = 0.75[/tex] --- This represents the rate per ride

The equation is the calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

So, we have:

[tex]y = 0.75(x - 0) + 12[/tex]

[tex]y = 0.75(x) + 12[/tex]

[tex]y = 0.75x + 12[/tex]

So, the cost function is:

[tex]C(x) = 0.75x + 12[/tex]

Calculate the cost of admission i.e. x=0

[tex]C(0) = 0.75*0 + 12=12[/tex]

So, we have:

[tex]C(0) =12[/tex] --- Admission Charge

[tex]C(x) = 0.75x + 12[/tex] --- Cost function

[tex]m = 0.75[/tex] --- Rate per ride

Ride C

No additional fee;

So, the cost function is;

[tex]C(x) = 30[/tex]

In summary, we have:

Ride A

[tex]C(x) =2x + 8[/tex] --- Cost function

[tex]m =2[/tex] --- Rate per ride

Ride B

[tex]C(x) = 0.75x + 12[/tex] --- Cost function

[tex]m = 0.75[/tex] --- Rate per ride

Ride C

[tex]C(x) = 30[/tex] --- Cost function

By comparison

Ride A has the highest rate per ride of (#2), followed by ride B with a rate  of #0.75 per ride.

Ride C has no charges per ride

The impact on the total cost is that:

Ride A: People that opt for ride A will pay the least to get admitted (i.e #8) but they pay the most (i.e. #2) per each ride they take

Ride B: People that opt for ride B will pay #12 to get admitted, but they pay 0.75 per each ride they take

For A and B, the overall cost depends on the number of rides taken.

Ride C: Irrespective of the number of rides taken, people that opt for ride C will pay the same flat fee of #30

Answer:

80

Step-by-step explanation:

Look at the figure below. The perimeter is the same as if the corners were moved out to form a square. Then you have 4 congruent sides of length 20.

P = 4 * 20 = 80

The perimeter of a shape is the summation of the sides of the shape. The perimeter of the shape is 80 units.

From the attached figure, we have the following observations

This means that if the shape is drawn (see attachment) to have 4 sides, opposite sides of the shape will be congruent.

The first side length is:

[tex]Length = 20[/tex]

While the adjacent side length is:

[tex]Width = 12 + 8 =20[/tex]

The perimeter (P) of the shape is then calculated as follows:

[tex]P = 2 \times (Length + Width)[/tex]

[tex]P = 2 \times (20 + 20)[/tex]

[tex]P = 2 \times 40[/tex]

[tex]P = 80[/tex]

Hence, the perimeter of the shape is 80 units.

Read more about perimeters at:

https://brainly.com/question/6465134

Answer:

m<ACB=1/2 of m<AOB

so m<ACB=45⁰÷2

m<ACB=22.5⁰

I HOPE IT HELPS HAVE NICE DAY!

Answer:

m<ACB=22.5° [as inscribed angle is half to the central angle]

Answer:

solution given;

length [l]=8in

breadth [b]=2in

height [h]=12in

we have

the surface area of the prism=2[lb+bh+lh]

=2[8×2+2×12+8×12]=272in²

272in² is your answer

Answer:

I worked it out and got 19339.64 but there is a high chance I could be wrong so maybe your right.

Answer: Monica

Step-by-step explanation:

Given

Monica has a 20% chance of winning a prize

Brianne has a  [tex]\frac{1}{10}[/tex] chance of winning a prize

20% chance refers to

[tex]\dfrac{20}{100}=\dfrac{2}{10}[/tex]

As

[tex]\dfrac{2}{10}>\dfrac{1}{10}[/tex]

therefore, monica is more likely to win the prize.

Answer:

4

Step-by-step explanation:

The given equation of circle is:

[tex] (x+2)^2 +(y-3)^2 =4 [/tex]

[tex] (x+2)^2 +(y-3)^2 =2^2 [/tex]

Equating it with:

[tex] (x-h)^2 +(y-k)^2 =r^2 [/tex]

We find:

[tex] r^2=2^2 [/tex]

[tex]\therefore r=2 [/tex]

Radius of the circle = 2 units

Therefore,

Diameter of the circle = 2*2= 4 units

Answer:

(

−

7

)

(

6

+

5

)

g0gf0g0g0

Answer:

94.5 days

Step-by-step explanation:

We are asked to calculate the time.

The formula to calculate the time for half life =

t = t½ × In (Nt/No)/-In2

t½ = half life = 16 days

No = Initial substance = 120mg

Nt = Amount of substances after time t = 2 mg

t = 16 × In (2/120)/-In2

t = 94.510249529736 days

Approximately = 94.5 days

Therefore, the time it would take for the substance to decay from 120mg to 2 mg is 94.5 days.

Answer:

there should be a "paper clip" sign

Step-by-step explanation:

then go to it click it and pick or take a photo

Answer:

[tex]( + 4h) {}^{2} \\ when \: h \: = 0 \\ (4 \times 0) {}^{2} \\ = 0[/tex]

Answer:

3 is answer .

follow me and help me

Answer:

D

Step-by-step explanation:

because 5 times 11 is 55. Times is also another word for multiplication.

Answer:

300

Step-by-step explanation:

6 × 10¹ ÷ 2 × 10-¹

= 300

no of aluminium is 300 times more than that of gold

Answer:

x=4

Step-by-step explanation:

the ones on top of each other you are adding together so -10x + -2x equals -12x and -32+-16 equals -48 and -48 divided by -12x equals positive 4

Answer:

Step-by-step explanation:

you can see from the picture that adding 2y and -2y cancels out. So the remaining parts of the equations are

-10x=-32

-2x=-16

add the two together:

-12x=-48

x=4

Answer:

I would think 1050 but I may be wrong

Answer:

Divide both sides by L

Step-by-step explanation:

Because L is multiplied by W, to find W you would need to move the L to the other side by doing the reverse operation, which in this case is division.

Answer:

9 gal

Step-by-step explanation:

Answer:

5x-27y=-2

Step-by-step explanation:

-2x+7x=5x

y-3y=-27y

0-2=-2

5x-27y=-2

Answer:

3.14

Step-by-step explanation:

area=pi times the square of radius

1^2 = 1 x 3.14=3.14

================================================================

Explanation:

If we were to keep the red curve completely fixed, but we moved the xy axis four units to the left, then this would give the illusion the red curve is moving four units to the right to arrive at the blue curve's location.

Shifting the xy axis four units to the left is the same as subtracting 4 from each initial input x value. So we go from x to x-4.

The parent function f(x) = x^2 then becomes g(x) = (x-4)^2 which is choice C.

As one way to check, plug in x = 4 and you should find that g(4) = 0. This is the x intercept of the blue curve. Something like g(x) = (x+4)^2 does not work because plugging x = 4 into this leads to g(x) = 64, so that rules out choice A. You can eliminate choices B and D for similar reasoning as well.

Answer:

C.) G(x) = ( x-4 )^2

Step-by-step explanation:

Took the test