In Prof. Leahy's class, if a student does homework most days, the chance of passing the course is 90%. On the other hand, if a student does not do homework most days, the chance of passing the course is only 30%. Prof. Leahy claims that 70% of his students do homework on a regular basis. If a student is chosen at random from Prof. Leahy's class, find the following probabilities:

a. p(the student did not do homework and he/she passed the course)
b. p(the student did not do homework given that she/he passed the course)

Solution:

Given data:

Distance from a point to the Peachtree Center Plaza in Atlanta, Georgia (base) = 340 feet

The angle of elevation to the top of the building = 65°

To find height of the building (perpendicular- p):

tan thetha = p/b

Tan 65°= h/340

tan 65°=2.144507

Now,

h= tan 65° * 340

 = 2.144507 * 340

 = 729.132 feet

So, the height of the building is 729.132 feet

Answer:

B. 3188.5 cubic inches.

Step-by-step explanation:

The volume of a cone is calculated using the following formula:

Volume = (1/3) * π * r² * h

Where:

In this problem, we are given that r = 17 inches and S.h = 20 inches.

First we need to find height h.

py using Pythagorous theorem,we get

c²=a²+b²

here c= slight height and a is radius

20²=17²+b²

20²-17²=b²

111=b²

b=√(111)

Plugging these values into the formula, we get:

Volume = ⅓*π* 17² *√(111) = 3188.5 cubic inches

Therefore, the volume of the cone is 3188.5 cubic inches.

The answer is, X = 12.

hope it helps.

Answer:

x = 12

Step-by-step explanation:

simlify 4/3 * (3x-12)

4x - 16 = 2x + 8

combine like terms, so subtract 2x by 4x

2x - 16= 8

then finish combining like terms, so 16 plus 8

2x = 24

divide 24 by 2

x = 12

The value of the expression 18 + 4(28) will be 130.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 18 + 4(28)

Simplify the expression, then the value of the expression will be

⇒ 18 + 4 x (28)

⇒ 18 + 4 x 28

⇒ 18 + 112

⇒ 130

Thus, the value of the expression 18 + 4(28) will be 130.

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The rearrangement of Tue following words to make a meaningful sentence is as follows:

A sentence is defined as the a group of words that is made up of a subject, a verb and punctuation marks which are used to create a meaning to the sentence.

The restructuring of the given sentence above would be shown below as follows:

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Step-by-step explanation:

The circumference of a WHOLE circle = pi * d

   you have 1/2 of this  and d = 10 ft

     so   1/2 pi * 10      PLUS the two straight sides + 8+6

       1/2 pi * 10   + 8 + 6

         5 pi + 8 + 6

        5 * 3.14   + 14 = 29.7 ft

Step-by-step explanation:

Answer:

The final temperature is 10.1 degrees Fahrenheit

The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:

A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.

A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.

A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.

A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.

B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.

B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.

Finally, performing the remaining operations:

(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.

(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.

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Answer:

-P is true.

Step-by-step explanation:

q v-p is false.

Starting with the given equation: 2 sin x cos x = cos x

By dividing both sides by cos x, we may simplify: 2 sin x = 1

Dividing both sides by 2:

sin x = 1/2

The values of x that fulfil sin x = 1/2 must now be found, and they are:

x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.

Therefore, the general solution is:

x = π/6 + 2πn or

x = 5π/6 + 2πn, where n is any integer.

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2x² - 6x = -7 equation has  imaginary solutions

To determine if an equation has imaginary solutions, we can examine the discriminant of the quadratic equation

x² + 3x - 5 = 0

a = 1, b = 3, c = -5

Discriminant = (3)² - 4(1)(-5) = 9 + 20 = 29

The equation has two real solutions

x⁴ - 5x ^ 2 + 3 = 0

This equation is a quartic equation, not a quadratic equation. Quartic equations can have both real and imaginary solutions

2x² - 6x = -7

2x^2 - 6x + 7 = 0

a = 2, b = -6, c = 7

Discriminant = (-6)²- 4(2)(7) = 36 - 56 = -20

Since the discriminant (-20) is negative, the equation has two complex (imaginary) solutions.

-3x² = -5

Dividing both sides by -3, we get:

x²= 5

a = 1, b = 0, c = -5

Discriminant = 0² - 4(1)(-5) = 20

The equation has two real solutions.

Hence, 2x² - 6x = -7 equation has imaginary solutions

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The equation which describes the relationship between the side length and shaded area of the quilt is y=0.5x²

Side length, x = 1,3,4,5,8

Shaded Area, y = 0.5, 4.5, 8, 12.5, 32

The relationship can be modeled as a quadratic function. Using a graphing calculator for the quadratic function written in the form y = ax² + bx + c

a = 0.5 ; b = 0 ; c = 0

Therefore, the quadratic function can be written as y = 0.5x²

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Answer:

3zx-15z+12x-60

Step-by-step explanation:

first do parenthesis and distribute (z+4)(x-5) into zx-5z+4x-20

then distribute the 3 to get the answer

Answer:

9/3=3

Step-by-step explanation:

3 goes into 9   3 times

3,6,9

Answer:

If you are using a cash register, giving back correct change is pretty simple. Just type in the cost of the item and the amount paid and bingo, the cash register tells you how much change to give back. However, if your cash register is broken, or you entered the wrong amount, or you don’t have a cash register, you’ll need to know how to make change on your own. The basic method is to count up from the price of the purchase to the amount the customer paid.

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Answer:

Ok

Step-by-step explanation:

The z-score for the raw score of 39 is 1.The z-score for the raw score of 30 is -0.8.Z-scores measure the number of standard deviations a raw score is from the mean. A positive z-score indicates a raw score above the mean, while a negative z-score indicates a raw score below the mean.

To find the z-scores, we need to use the formula:

z = (x - μ) / σ

where:

z is the z-score,x is the raw score,μ is the mean, andσ is the standard deviation.

Let's calculate the z-scores for the given mean of 34 and standard deviation of 5.For a raw score of 39:

z = (39 - 34) / 5

z = 5 / 5

z = 1

So, the z-score for the raw score of 39 is 1.For a raw score of 30:

z = (30 - 34) / 5

z = -4 / 5

z = -0.8

The z-score for the raw score of 30 is -0.8.

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The probability that the mean amount of cereal in 5 randomly selected boxes is at most 9.65 ounces is 0.4808.

The Central limit theorem is used to find the probability

Data given:

sample size = 5.

mean, μ = 9.70 ounces

standard deviation, σ = 0.03 ounce.

To calculate the probability, we determine the z-score corresponding to the sample mean of 9.65 ounces using the z-score formula.

x is the sample mean,

μ is the population mean,

σ is the population standard deviation, and

n is the sample size.

For the sample mean of 9.65 ounces in 5 boxes:

z = (9.65 - 9.70) / (0.03 / √5)

z ≈ -0.05 / (0.03 / √5)

Using a calculator, we find that the probability is approximately 0.4801.

Therefore, the probability that the mean amount of cereal in 5 randomly selected boxes is less than 9.65 ounces is approximately 0.4801.

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Answer:

no, Andre ran at a sperm of 8km/hr while jada ran at 9km/hr you can find that by Andre going 2km in 15 minutes which turns to hours by multiplying by 4/4 to get 8/60 which 60 minutes is 1 hour then jada multiply by 3/3 which would be 9/60

Mel must serve a minimum of 6 tables per hour to earn more than $25 per hour.

Here, we are given that Mel uses the linear expression (4x + 5) to calculate his hourly earning, in dollars. Here x = number of tables served.

If he wants to earn $25 per hour then the value of the linear equation must be equal to 25. This means-

4x + 5 = 25

4x = 25 - 5

4x = 20

x = 20/ 4

x = 5

Now, if he wants to earn more than $25 per hour, he must serve more than 5 tables. This implies that he must as least serve 6 tables.

Thus, Mel must serve a minimum of 6 tables per hour to earn more than $25 per hour.

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I'm confused, I'm not sure if the 12 you added to the problem is like the number of the problem or part of the problem, but my answer is going to be with the 12 as part of the problem.

Answer:  19/4 or 4 3/4 or 4.75

Step-by-step explanation: First you have to use the PEMDAS, which means first you have to do the parenthesis first, so add the 1/4 to the 1/3 which equals 7/12. so do that to the second power and then multiply the 12 and add the 2/3 which gets you 19/4

Answer:

The requirements that are necessary for a normal probability distribution to be a standard normal probability distribution are µ = 0 and σ = 1.

Step-by-step explanation:

A normal-distribution is an accurate symmetric-distribution of experimental data-values.  

If we create a histogram on data-values that are normally distributed, the figure of columns form a symmetrical bell shape.  

If X \(\sim\) N (µ, σ²), then \(Z=\frac{X-\mu}{\sigma}\), is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z \(\sim\) N (0, 1).

The distribution of these z-variates is known as the standard normal distribution.

Thus, the requirements that are necessary for a normal probability distribution to be a standard normal probability distribution are µ = 0 and σ = 1.

Answer:

604800

Step-by-step explanation:

Answer:so the answer is 1,9,7,3,5,2

Step-by-step explanation:

The set of all possible outcomes is S = {A, C, G, T}. The set of all possible outcomes is also called the sample space. Events of interest might be E1 = an A

The woman will withdraw $300 given 6%   interest rate annually.

We can use the formula for simple interest to solve this problem:

I = Prt

where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years. Since the interest rate is given as an annual rate, we need to convert it to a daily rate by dividing by 365:

r = 0.06/365 = 0.00016438356

The time in years is 120/365 = 0.3287671233 years. Now we can plug in the values and solve for I:

I = 300 * 0.00016438356 * 0.3287671233 = 0.01699999999

The interest earned is $0.017, which is negligible. Therefore, the woman will withdraw the entire principal plus any interest earned, which is:

300 + 0.017 = $300.02

Rounding to the nearest dollar, the woman will withdraw $300.

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i dont know. Im sorry about that.

The common ratio in the sequence is √581/3

We know that in a geometrical progression with a common ratio R, the recursive formula is:

A(n)  = R*A(n - 1)

That means that each term in the sequence is R times the previous term, so knowing one term and R (or two terms) we can completely define the sequence.

Here we know that:

A(3) = 18

A(5) = 1162

Then we could write:

A(5) = R^2*A(3)

1162 = 18*R^2

1162/18 = R^2

581/9 = R^2

√(581/9) = R

√581/3  =R

That is the common ratio.

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