Math 1314 lab module 2

a) P(k≤11) = 0.021 b) P(k>23) = 0.213 c) P(11≤k≤23) = 0.777 P(11<k d="" p="" step-by-step="" explanation:="" a="" what="" is="" the="" probability="" that="" number="" of="" drivers="" or="" fewer="" we="" will="" compute="" b="" exceeds="" this="" can="" be="" defined="" as:="" c="" lies="" between="" and="" including="" both="" ends="" about="" strictly="" for="" inclusive="" range:="" exclusive="" likelihood="" falls="" within="" standard="" deviations="" mean="" deviation="" needed="" next="" alongside="" computation="" />

Answer: 23 y 24 ( ó -23 y -24)

Step-by-step explanation:

Two consecutive numbers can be represented as:

n y (n + 1)

where n is an integer.

Hence, "The product of two consecutive numbers is 552" can be expressed as:

n*(n + 1) = 552

n^2 + n = 552

n^2 + n - 552 = 0

We have a quadratic equation, and the possible solutions are obtained using the Bhaskara formula.

The two solutions are:

n = (-1 - 47)/2 = -48/2 = -24

n = (-1 + 47)/2 = 46/2 = 23

If we take the first solution, n = -24

Then the two consecutive numbers would be:

n = -24

(n + 1) = -23

If n = 23, then

n + 1 = 24

Which makes sense, as the only change is the signs, which would negate each other in multiplication.

Response:

Move 2 units to the left

Reflect the graph across the y-axis

Expand horizontally by a factor of 2

Lift vertically by 2 units

Detailed explanation:

Provided:

Basic function:

Transformed function:

Extract -2 from the transformation function f(x)

Now, we can observe the step-by-step transformations

Move 2 units to the left ( x → x+2 )

Reflect the graph across the y-axis ( (x+2) → - (x+2) )

Expand horizontally by a factor of 2 [ -x(x+2) → -2(x+2) ]

Lift vertically by 2 units [ f(x) → f(x) + 2 ]

Simplifying the function:

Thus, applying four transformation steps results in the new function

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.

Sample Answer: No, Ingrid's statement is incorrect. In this situation, the starting point is at 170 feet, which denotes the y-intercept. The reduction of 4 feet per year symbolizes the rate of change, or slope. In the slope-intercept equation format, y = mx + b, with 'm' denoting the slope and 'b' signifying the y-intercept, the accurate equation would be y = −4x + 170.