When do creative people get their best ideas? USA Today did a survey of 966 inventors (who hold U.S. patents) and obtained the following information.

Time of Day When Best Ideas Occur
Time Number of Inventors
6 A.M.-12 noon 271
12 noon-6 P.M. 123
6 P.M.-12 midnight 327
12 midnight-6 A.M. 245

Required:
a. Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a best idea during each time interval: from 6 A.M. to 12 noon, from 12 noon to 6 P.M., from 6 P.M. to 12 midnight, from 12 midnight to 6 A.M.
b. Do the probabilities add up to 1? Why should they?

Answers

Answer 1

Answer:

a.

0.2805 = 28.05% probability that an inventor has a best idea from 6 A.M. to 12 noon.

0.1273 = 12.73% probability that an inventor has a best idea from 12 noon to 6 P.M.

0.3385 = 33.85% probability that an inventor has a best idea from 6 P.M. to 12 midnight.

0.2536 = 25.36% probability that an inventor has a best idea from 12 midnight to 6 A.M.

b. They do, as the the sum of the probabilities of all possible outcomes should be 1, as is in this question.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the total outcomes.

We have:

A total of 966 inventors.

Question a:

6 A.M. to 12 noon

271 out of 966, so:

[tex]p = \frac{271}{966} = 0.2805[/tex]

0.2805 = 28.05% probability that an inventor has a best idea from 6 A.M. to 12 noon.

12 noon to 6 P.M.

123 out of 966, so:

[tex]p = \frac{123}{966} = 0.1273[/tex]

0.1273 = 12.73% probability that an inventor has a best idea from 12 noon to 6 P.M.

6 P.M. to 12 midnight

327 out of 966, so:

[tex]p = \frac{327}{966} = 0.3385[/tex]

0.3385 = 33.85% probability that an inventor has a best idea from 6 P.M. to 12 midnight.

12 midnight to 6 A.M.

245 out of 966. So

[tex]p = \frac{245}{966} = 0.2536[/tex]

0.2536 = 25.36% probability that an inventor has a best idea from 12 midnight to 6 A.M.

b. Do the probabilities add up to 1? Why should they?

0.2805 + 0.1273 + 0.3385 + 0.2536 = 1

They do, as the the sum of the probabilities of all possible outcomes should be 1, as is in this question.


Related Questions

what is the ordered pair for the equation -7x+3y=2​

Answers

Answer:

Step-by-step explanation:

X/30 + X/40= 1
Solve for x

Answers

Answer:

17 1/7 I think

Step-by-step explanation:

x=17.1

Step-by-step explanation:

[tex] \frac{x}{30} + \frac{x}{40} = 1 \\ \frac{3x + 4x}{120} = 1 \\ \frac{7x}{120} = 1 \\ \frac{7x}{120} = 1 \\ 7x = 120 \\ x = \frac{120}{7} \\ x =17.1 [/tex]

Po is an oncologist with seven patients in their care. the probability that a patient will survive five years after being diagnosed with stage three breast cancer is 0.82. what is the probability that four of the patients are still alive after five years?

Answers

Answer:

0.0923 = 9.23% probability that four of the patients are still alive after five years.

Step-by-step explanation:

For each patient, there are only two possible outcomes. Either they are still alive after five years, or they are not. The probability of a patient being alive is independent of any other patient, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Po is an oncologist with seven patients in their care.

This means that [tex]n = 7[/tex]

The probability that a patient will survive five years after being diagnosed with stage three breast cancer is 0.82.

This means that [tex]p = 0.82[/tex]

What is the probability that four of the patients are still alive after five years?

This is P(X = 4). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{7,4}.(0.82)^{4}.(0.18)^{3} = 0.0923[/tex]

0.0923 = 9.23% probability that four of the patients are still alive after five years.

Solve the system.
2x + y = 3 −2y = 14 − 6x

Answers

Answer:

(x , y ) = (39/22 , -2/11 )

.............

Answer:

-2,3 3,-7

Step-by-step explanation:

took test :)

During a football game, a team lost 9 yards on the first play, then gained 3 yards on each of the next 3 plays. Which
integer represents the total number of yards at the end of the first four plays?
оооо
9
18

Answers

They lost 9 and gained nine so the did not move still in the same spot

you and your friend start biking to opposite directions from the same point. You travel 108 feet every 8 seconds. Your friend travels 63 feet every 6 seconds. a) how far apart are you and your friend after 15 minutes? b) after 20 minutes you take a 5- minutes rest, but your friend does not. How far apart are you and your friend after 40 minutes? Explain your reasoning.

Answers

Answer:

To find your distance apart, you can convert 15 minutes to seconds because that is what the rate is given in.

15 mins x 60 seconds = 900 seconds.

Step-by-step explanation:

In 900 seconds, there are 900/8=112.5 groups of 8 seconds. This means there are 112.5 groups of 108 feet.

112.5 x 108 = 12150 feet

12150 feet/5280 feet is approximately 2.3 miles.

For your friend you take 900/6 = 150 groups of 6 seconds.

150 x 63 = 9540 feet

9540 feet/5280 feet = 1.79 miles

1.79 miles + 2.3 miles = 2.09 miles

You and your friend are about 2.09 miles apart after 15 minutes.

B). If you go 2.3 miles every 15 minutes, that means you travel about 0.77 miles every 5 minutes. If you travel 20 more minutes (40-15-5) that would be 0.77x 4=3.07 miles more

3.07 + 2.3 = 5.37 miles after 40 minutes (you).

Your friend travels 1.79 in 15 minutes, so 1.79/3 = 0.6 miles every 5 minutes

0.6 x 5 (5 x 5 = 25 minutes)= 3 miles

1.79 + 3 miles= 4.79 miles (friend)

4.79 + 5.37 = 10.16 miles

You and your friend are about 10.16 miles apart after 40 minutes.

(3x^ - 6x +11) - (10x^ - 4x + 6)

Answers

Answer:

3x−6x+11−(10x−4x+6)

=5x10−10x7+3x5

         x10

=5x5−10x2+3

      x5

Step-by-step explanation:

i hope this helps and i hope you understand this, sorry if you dont understand

Suppose that E and F are points on the number line.
If EF=9 and E lies at 4, where could F be located?
If there are several locations, separate them with commas.

Answers

9514 1404 393

Answer:

  -5 or 13

Step-by-step explanation:

A point that is 9 units from 4 on the number line ca be located at ...

  4 - 9 = -5

  4 + 9 = 13

F could be either of -5, 13.

help
Sadie needs 3.1 yards to make one costume for each choir member in the play. How much fabric will she need if she has to make 5 costumes?
A.
15.5 yards
B.
10.5 yards
C.
18.6 yards
D.
16.5 yards

Answers

Answer:

A. 15.5 yards

Step-by-step explanation:

3.1 ×5=15.5

Cannot seem to figure this one out.

Answers

Answer:

cosB = 2√6 / 7

Step-by-step explanation:

use the pythagorean theorem to find the missing side

a² + b² = c²

a² + 5² = 7²

a² + 25 = 49

a² = 24

a = √24

a = 2√6

--------------------------

cosB = adj/hyp

cosB = 2√6 / 7

The length of a rectangle is six times its width.
If the perimeter of the rectangle is 84 in, find its area.

Answers

Answer:

6yd=W The width of the rectangle is 6 yards. L=6W=6(6yd)=36 yards The length is 36 yards. A=36yd*6yd=216 sq yd ANSWER: The area is 216 square yards...

The area of a given rectangle is 216 square inches.

Given that, the perimeter of the rectangle is 84 inches.

We need to find the area of a rectangle.

What is the perimeter of a rectangle?

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Let the width of a rectangle be x.

Given, that the length of a rectangle is six times its width. So, length=6x.

Now, 84=2(6x+x)

⇒14x=84

⇒x=6 inches

Then, length=6x=36 inches.

Area of a rectangle= Length×width=36×6=216 square inches

Therefore, the area of a given rectangle is 216 square inches.

To learn more about the area of a rectangle visit:

https://brainly.com/question/20693059.

#SPJ2

Pls Pls Pls help! Simplify the equation: [tex]\sqrt{\frac{1}{9} x^{2}y^{10}[/tex]

Answers

the answer is xy^5/3 .

What is the product?
(-282 +8)(502-65)

Answers

Answer:

option c is the answer for pic

and for question the answer is

(-274)*(437)

-119738

Answer:

the first one

Step-by-step explanation:

convert 122f to Celsius​

Answers

Answer:

50°C

Step-by-step explanation:

(122°F − 32) × 5/9 = 50°C

What is
(481x10")(1.1x 10-4) in scientific notation?
5.291x 10-64
5.291x10
5.291x1012
5.291x1020

Answers

Answer:

5.291 * 10^4

hhhhhhhhhhhhhhhhh

Find the distance between the pair of points: (2,6) and (0,−3).

Answers

Answer:

d = √85

Step-by-step explanation:

d^2 = (X2 - X1)^2 + (Y2 - Y1)^2

= (2 - 0)^2 + (6 + 3)^2

= 4 + 81

d = √85

What is the equation of a circle with center (4, 4) and radius 7?

Answers

Answer:

(x-4)^2 + (y-4)^2 = 49

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2  where ( h,k) is the center and r is the radius

(x-4)^2 + (y-4)^2 = 7^2

(x-4)^2 + (y-4)^2 = 49

5(x+2)-4 = 13-7(x+1)

Answers

Answer:

0

Step-by-step explanation:

5x+10-4=13-7x-7

5x+6=6-7x

5x+0= -7x

0=-12x

Divide and u get x=0

VERY URGENT
The sum of two numbers is 36. The smaller number is 18 less than the larger number. What are the numbers?
Larger number:
Smaller number:

Answers

Answer:

Larger number: 22

The smaller number: 14

HOPE THIS HELPS

Which of the following is the product of 7/8 and -4/21?  a.- 1/6 b.1/12 c.- 16/21 d.- 147/32​

Answers

Answer:

A. -1/6

Step-by-step explanation:

7/8 × -4/217 can be divided by 21 wich will make the fraction -4/21 turn to -4/3 and the fraction 7/8 turn to 1/8-4 can be divided by eight which will make the fraction 1/8 turn to 1/2 and the fraction -4/3 will turn to -1/31/2 × -1/3 = -1/6

The product of 7/8 and -4/21 is a.- 1/6.

What is the product?

In mathematics, a product is the result of multiplication, or an expression that identifies factors to be multiplied.

Now the given numbers are,

7/8 and -4/21

now taking 7/8 and since 8= 4*2

so, 7/8 = 7/(4*2)

Again taking -4/28 and since 28 = 7*4

so, -4/21 = -4/(7*3)

hence the product of 7/8 and -4/21 is given as,

7/8*(-4/21) = 7/(4*2) x -4/(7*3)

taking alike terms together we get,

7/8*(-4/28) = (7/7)(4/4)(-1/2*3)

⇒ 7/8*(-4/28) = -1/6

Hence the correct option is a.-1/6

Therefore,The product of 7/8 and -4/21 is a.- 1/6.

Learn more about product :

https://brainly.com/question/1549083

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Find the value of x to the nearest degree.
16
7
Not drawn to scale

Answers

Answer:

66°

Step-by-step explanation:

Given the right angled triangle :

Opposite side = 16

Adjacent side = 7

Using trigonometric relation :

Tan θ = opposite / Adjacent

Tan x = (16/7)

x = tan^-1(16/7)

x = 66.37°

x = 66°

1 Joseph weighs 100 pounds and his sister weighs 100 pounds. How much do they weigh together? 15 a. 4 200 pounds 4 100 15 15 pounds b. d. 2 200 pounds 20 5 200 pounds 15 Please select the best answer from the choices provided O A OB Ос D​

Answers

Your answer is going to be a
A because 100+100 is 200

PT=3x+3 and TQ=6x-6
Use the figure to the right to find the value of PT. T is the midpoint of PQ

Answers

Answer:

PT = 12 units

Step-by-step explanation:

Given that,

PT=3x+3 and TQ=6x-6

T is the midpoint of PQ.

If T is mindpoint of PQ, it means,

PT = TQ

Substitute all the values,

3x+3 = 6x-6

Taking like terms together,

3x-6x = -6-3

-3x = -9

x = 3

So,

PT = 3x+3

= 3(3) + 3

= 9+3

= 12

So, the value of PT is equal to 12 units.

PLEASE HELPPPP ASAP PLS WILL MARK BRAINLIEST

Answers

Answer:

5X+6+3X-2 =180

8X+4. =180

8X. =180-4

8X. =176

X=22

CBD=EBF=3x-2

=66-2

=64

CBD=64

HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

The solution set to the absolute value is:

[tex]S = \{x \in \mathbb{R}| x \ge 0\}[/tex] or [tex]S = [0, +\infty)[/tex]

Negative real numbers are not included in the solution set, as for [tex]x < 0[/tex], [tex]|x| = - x[/tex].

Step-by-step explanation:

From Mathematics, we know that absolute values are defined by the following characteristics:

1) For [tex]x \ge 0[/tex], [tex]|x| = x[/tex]

2) For [tex]x < 0[/tex], [tex]|x| = - x[/tex]

Then, if [tex]|x| = x[/tex], then the solution set to the absolute value is:

[tex]S = \{x \in \mathbb{R}| x \ge 0\}[/tex] or [tex]S = [0, +\infty)[/tex]

Negative real numbers are not included in the solution set, as for [tex]x < 0[/tex], [tex]|x| = - x[/tex].

Which graph shows Point Pin Quadrant II and Point Q as (3,-4)

Answers

Answer:

p would be up top on the negative side (left)

q would be at the bottom on the positive side (right)

In exponential smoothing, the equation involves what type of value that is not part of the moving averages equation?
a. Upper limit
b. Lower limit
c. Level smoothing constant
d. Recent observed value

Answers

Answer:

d. Recent observed value

Step-by-step explanation:

Exponential smoothing is technique for smoothing time series data. In exponential smoothing more recent observed values give larger weights while the weights will decline if observed values are more distant. In moving average the observations were weighted equally.

Use the Squeeze Theorem ​

Answers

Answer:

See Below.

Step-by-step explanation:

We want to use the Squeeze Theorem to show that:

[tex]\displaystyle \lim_{x \to 0}\left(x^2\sin\left(\frac{2}{x}\right)\right)=0[/tex]

Recall that according to the Squeeze Theorem, if:

[tex]\displaystyle g(x)\leq f(x) \leq h(x)[/tex]

And:

[tex]\displaystyle \lim_{x\to c}g(x) =\lim_{x\to c}h(x) = L[/tex]

Then:

[tex]\displaystyle \lim_{x\to c}f(x)=L[/tex]

Recall that the value of sine is always ≥ -1 and ≤ 1. Hence:

[tex]\displaystyle -1 \leq \sin\left(\frac{2}{x}\right) \leq 1[/tex]

We can multiply both sides by x². Since this value is always positive, we do not need to change the signs. Hence:

[tex]\displaystyle -x^2\leq x^2\sin\left(\frac{2}{x}\right)\leq x^2[/tex]

Let g = -x², h = x², and f = x²sin(2 / x). We can see that:

[tex]\displaystyle \lim_{x \to 0}g(x) = \lim_{ x \to 0}h(x) = 0[/tex]

And since g(x) ≤ f(x) ≤ h(x), we can conclude using the Squeeze Theorem that:

[tex]\displaystyle \lim_{x \to 0}f(x) = \lim_{x \to 0}x^2\sin\left(\frac{2}{x}\right)=0[/tex]

4. If your balance on an investment of $100 that has been invested at
a rate of 7.5% is $178.35 at the end of 8 years, does the plan have simple
interest or compound interest?

Answers

Answer:

Simple interest

Step-by-step explanation:

Because its a period of 8 years

lab scale known to have a standard deviation of 0.001gram, speimen weghtted 8 times. average weiht is 4.1602 gram. what is 99% confidence interval

Answers

Answer:

[tex]99\% CI=4.1602 \pm 0.0009[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=8[/tex]

Mean [tex]\=x=4.1602[/tex]

Standard deviation [tex]\sigma=0.001gram[/tex]

Generally 99\% confidence from table  is mathematically given by

 [tex]99\% CI=4.1602 \pm *2.576*\frac{0.001}{\sqrt{{8}}}[/tex]

 [tex]P(-z<x<z)=0.99[/tex]

 [tex]Z_{\alpha/2}=2.576[/tex]

Generally the equation for 99\% confidence level (CI)  is mathematically given by

 [tex]99\% CI=\=x \pm Z_{\alpha/2*\frac{\sigma}{\sqrt{{n}}}[/tex]

 [tex]99\% CI=4.1602 \pm 0.0009[/tex]

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