Consider the two triangles. Triangles A B C and H G I are shown. Angles A C B and H I G are right angles. The length of side A C

Answer:

a) There is a 99.73% chance that a randomly picked individual does not celebrate their birthday on March 14.

b) There is a 96.71% chance that a randomly picked individual does not celebrate their birthday on the 2nd day of any month.

c) There is a 98.08% chance that a randomly picked individual does not celebrate their birthday on the 31st day of a month.

d) There is a 92.33% chance that a randomly picked individual was not born in February.

Step-by-step explanation:

The probability is calculated as the number of successful outcomes divided by the total outcomes.

A standard year comprises 365 days.

(a) Calculating the probability that a randomly selected individual does not have a birthday on March 14:

Excluding March 14 yields 365-1 = 364 days. Thus,

364/365 = 0.9973

So, there is a 99.73% chance that a randomly selected person does not celebrate their birthday on March 14.

(b) Calculating the probability that a randomly selected person does not celebrate their birthday on the 2nd day of a month:

With 12 months, there are 12 occurrences of the 2nd day.

Thus,

(365-12)/365 = 0.9671

Hence, a 96.71% chance that someone does not have a birthday on the 2nd day of any month.

(c) Calculating the probability that a randomly chosen individual does not have a birthday on the 31st day of any month:

Months with 31 days include January, March, May, July, August, October, and December.

This totals 7 instances of the 31st day.

Thus,

(365-7)/365 = 0.9808

In conclusion, there's a 98.08% chance that a randomly selected person does not celebrate their birthday on the 31st day of any month.

(d) Calculating the probability that a randomly selected person was not born in February:

February has 28 days in a non-leap year. Thus,

(365-28)/365 = 0.9233

So, a 92.33% chance that a randomly picked individual was not born in February.

Response:

The bike positioned higher on the y-axis is the one that has traveled a greater distance.

Step-by-step explanation:

If Dorrian charted the positions of the bikes with time in seconds on the x-axis and distance traveled on the y-axis, the x-coordinates for both bikes would align.

However, the bike that finished faster would achieve a higher y-coordinate, while the slower one trail behind with a lower y-coordinate.

Thus, the bike with the higher y-coordinate is the victor of the race.

Question

Consider this system of equations. Which shows the second equation written in slope-intercept form?

A.

B.

C.

D.

Response:

B.

Detailed explanation:

Given

Equation 1:

Equation 2:

Required:

Equivalent of equation 2

To achieve an equivalence of equation 2 (in slope-intercept form), we must first simplify it

Open the brackets

Simplify the fractions

Divide by 2

Re-arrange

Next, we compare options A through D with

A. is not equal to

Next, we check the second option

B.

matches

This option represents the second equation in slope-intercept format.

We check for further options

C.

Convert the fraction into a decimal

This does not equal

D.

Convert the fraction to decimal

This also does not equal to

Therefore, the only option equivalent to the second equation in slope-intercept form is Option B

It appears you've gathered most of the relevant information, but a critical element is missing. The surface represented is parameterized by... and has a normal vector corresponding to this representation with a specified norm. Thus, the integral of... is...

Answer:

Step-by-step explanation:

The prices he received quotes for are as follows: $663, $273, $410, $622, $174, $374

To begin, we will find the average.

Average = total of data points/ number of data points.

Total of data points =

663 + 273 + 410 + 622 + 174 + 374

= 2516

Total count = 6

Average = 2516/6 = 419.33

Standard deviation = √summation(x - m)^2/n

summation(x - m)^2/n = (663 - 419.33)^2 + (273 - 419.33)^2 + (410 - 419.33)^2 + (622 - 419.33)^2 + (174 - 419.33)^2 + (374 - 419.33)^2

= 179417.9334/6 = 29902.9889

Standard deviation = √29902.9889

= 172.9