A board 120 inches long is divided into 2 sections. If the ratio of the 2 sections is 3:5, what are the lengths of the sections?
15 inches, 105 inches
A
B
24 inches, 96 inches
C 40 inches, 80 inches
D 45 inches, 75 inches

Using the normal distribution, it is found that:

a) 4.46% of finish times was higher than 72 minutes.

b) 55.11% of finish times was between 52 and 70 minutes.

c) The 40th percentile of finish times is 52.5 minutes.

d) The 95th percentile of finish times is 71.45 minutes.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item a:

The proportion is 1 subtracted by the p-value of Z when X = 72, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{72 - 55}{10}[/tex]

[tex]Z = 1.7[/tex]

[tex]Z = 1.7[/tex] has a p-value of 0.9554

1 - 0.9554 = 0.0446

0.0446 x 100% = 4.46%

4.46% of finish times was higher than 72 minutes.

Item b:

Th proportion is the p-value of Z when X = 70 subtracted by the p-value of Z when X = 52, hence:

X = 70:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70 - 55}{10}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a p-value of 0.9332.

X = 52:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{52 - 55}{10}[/tex]

[tex]Z = -0.3[/tex]

[tex]Z = -0.3[/tex] has a p-value of 0.3821.

0.9332 - 0.3821 = 0.5511

0.5511 x 100% = 55.11%

55.11% of finish times was between 52 and 70 minutes.

Item c:

The 40th percentile is X when Z has a p-value of 0.4, so X when Z = -0.253.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.253 = \frac{X - 55}{10}[/tex]

[tex]X - 55 = -0.253(10)[/tex]

[tex]X = 52.5[/tex]

The 40th percentile of finish times is 52.5 minutes.

Item d:

The 95th percentile is X when Z has a p-value of 0.95, so X when Z = 1.645.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.645 = \frac{X - 55}{10}[/tex]

[tex]X - 55 = 1.645(10)[/tex]

[tex]X = 71.45[/tex]

The 95th percentile of finish times is 71.45 minutes.

A similar problem is given at https://brainly.com/question/24663213

Answer:

I have a couple questions before I answer, what do the 2 dashes represent and are the 4s also under the square root?

Answer:

3.375

Step-by-step explanation:

Answer:

The amount before the tip was $12.58

Step-by-step explanation:

Answer:

The amount before the tip was $12.58

Step-by-step explanation:

The place value of 7 in words in 5.3479 is seven thousandths

The given number is 5.3479

The underlined digit has been identified as 7

The place values of each of the digits in 5.3479 are:

5 = 5 units

3 = 3 tens

4 = 5 hundredths

7 = 7 thousandths

9 = 9 ten thousandths

Therefore, the place value of 7 in words in 5.3479 is seven thousandths

Learn more here: https://brainly.com/question/25750254

Answer:

x² + 10x + 25

Step-by-step explanation:

(x + 5)(x + 5)

using FOIL method

First x•x = x²

Outside x•5 = 5x

Inside 5•x = 5x

Last  5•5 = 25

add like terms together.

Answer:

x^2 + 25 + 10x

= x^2 + 10x + 25

Step-by-step explanation:

( x + 5 )^2

Formula : -

( a + b )^2 = a^2 + b^2 + 2ab

Here,

a = x

b = 5

( x + 5 )^2

= x^2 + 5^2 + 2 ( x ) ( 5 )

= x^2 + 25 + 10x

Answer:

2.66666666667

or

266666666667/100000000000

Step-by-step explanation:

9514 1404 393

Answer:

  2 2/3

Step-by-step explanation:

The minus signs cancel, so the sum is ...

  4/2 +2/3

The improper fraction on the left reduces to 2, so this is ...

  2 +2/3

That sum is simply the mixed number 2 2/3.

Answer:

I dont but want to.

Hope this helps! :) ;-;

Step-by-step explanation:

Answer:

6384 is the exact answer.

6000 is the answer rounded to the nearest thousand

Step-by-step explanation:

Answer:

6000

Step-by-step explanation:

532 X 12 = 6384 rounded would be 6000 miles a yr

Answer:

15/164

Step-by-step explanation:

5/8 ÷ 6 5/6 = 5/8 ÷ 41/6

                   = 5/8 x 6/41

                   = 30/328

                   = 15/164

Answer:

4(11+8+28)

Step-by-step explanation:

44 + 32 + 112

4(11+8+28)

I found the GCF of all three numbers.

Hope this helps :)

3

Step-by-step explanation:

i need help to

Answer:

Make it an improper fraction and multiply by 100

Answer:

Well a percent means out of a hundred

And a mixed number is

x e/y (example)

Now we know the whole number is already 1 and above so we know that’s already a 100%

Now we just need to add the other fraction to the 100%.

Thats it!

OR you can do convert the mixed number into an improper fraction.

From there make a proportion of the improper fraction equaling x/100

Now solve the proportion by cross multiplying.

Solve for x

Answer:

315 jars

Step-by-step explanation:

This question is merely another way of writing: what is 35% of 900?

Now, when we look at it that way, it's easy to solve.

So, the way to solve is to either multiply 35% by 900, or just interpret that as 0.35 times 900. Anyway, the result is 315.

I hope this helped a bunch! Tell me if you need any further assistance...

( :

Answer:

[tex]7+3^{2} - 2[/tex] × [tex]5 < (\frac{3}{4} + \frac{1}{8} )[/tex] ÷ [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

so <

hope this helps!

Answer:

250

Step-by-step explanation:

You can take the explicit formula and simply substitute the n value with 64:

-2 + 4 * (64 - 1)

-2 + 4 * (63)

-2 + 252

250

Answer:

[tex]f(x) = \left \{ {{x + 3} \quad \text{if} \ -3 \leq x < -1\atop {5} \quad \text{if} \ -1 \leq x \leq1} \right.[/tex]

Step-by-step explanation:

You can find the first function if you know the general form of a line:

[tex]y = mx + b[/tex]

where [tex]m[/tex] is the slope and [tex]b[/tex] the intercept point with the [tex]y[/tex]-axis.

So in the first case the slope is 1 because the next formula

[tex]m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2-0}{-1+3} = 1[/tex]

And you can find the interception point if extend the line, then in our case is  3.

So the function is:

[tex]f(x) = x + 5[/tex]

In the other case is constant function that's mean that the function has the next form

[tex]f(x) = k[/tex]

Where [tex]k[/tex] is a constant.

So you only have to observe what is the value for each point in the interval, in this occasion is 5.

So the final answer is:

[tex]f(x) = \left \{ {{x + 3} \quad \text{if} \ -3 \leq x < -1\atop {5} \quad \text{if} \ -1 \leq x \leq1} \right.[/tex]

Answer:

the answer is A

Step-by-step explanation:

Answer:

41 litters to gallons is 10.8311

3.5 gallons to litters is 13.2489

A = 10.8311 Gallons

B = 13.2489 Literes

Answer:

27/20

Step-by-step explanation:

¾ + ³/5= 27/20. .......................

Answer:

Step-by-step explanation:

Let x represent the amount invested at 4% (the higher rate). Then the amount invested at 3% is (6000-x), and the total interest earned is ...

  0.04x + 0.03(6000 -x) = 216

  0.01x +180 = 216 . . . . simpilfy

  0.01x = 36 . . . . . . . . subtract 180

  x = 3600 . . . . . . . . multiply by 100

  6000-x = 2400

Katie invested $3600 at 4% and $2400 at 3%.

Step-by-step explanation:

the numbers : x, y

x + y = 8

x = y - 4

we use the second equation in the first :

y - 4 + y = 8

2y - 4 = 8

2y = 12

y = 6

x = y - 4 = 6 - 4 = 2

Answer: The answer is 6 and 2

Step-by-step explanation:

X is first number, Y is second

x + x - 4 = 8

2x = 12

x = 6

Y = x - 4

Y = 6 - 4

Y = 2

x = 6

Y = 2

Answer:

23

if you have 15 gallons of gas and it makes it 345 miles that is 345 divided by 15 which is 23 or 023

15x2 equals 30 34 - 30 equals 4 bring the 5 down you have 45 15x3 equals 45, 45 - 45 equals 0

Answer:

This means that b is not equal to -10.

Answer:

9

Step-by-step explanation:

Please Excuse My Dear Aunt Sally

Answer:

= 10x − 1

Step-by-step explanation:

Let's simplify.

2 + 2x(5) − 3

= 2+10x + −3

Combine Like Terms:

= 2 + 10x + −3

= (10x) + (2 + −3)

= 10x + −1

= 10x − 1