Using the sum or difference formulas,how do we find the exact value of sin (285°)?

To solve this problem, we make use of the binomial probability equation.

P = [n! / (n – r)! r!] p^r * q^(n – r)

where,

n is the total number of sample = 100,000

r is the number of people with rare blood disorder = 7 or more

p is success of having a disorder = 0.00004

q is 1- p = 0.99996

But since it is easier to solve for the sum of probabilities with 0 to 6 disorder then deduct it from 1.

So,

=> at r = 0

P (r = 0) = [100,000! / (100,000 – 0)! 0!] (0.00004)^0 * (0.99996)^(100,000 – 0)

P (r = 0) = 0.01831

=> at r = 1

P (r = 1) = [100,000! / (100,000 – 1)! 1!] (0.00004)^1 * (0.99996)^(100,000 – 1)

P (r = 1) = 0.07326

=> at r = 2

P (r = 2) = [100,000! / (100,000 – 2)! 2!] (0.00004)^2 * (0.99996)^(100,000 – 2)

P (r = 2) = 0.14652

=> at r = 3

P (r = 3) = [100,000! / (100,000 – 3)! 3!] (0.00004)^3 * (0.99996)^(100,000 – 3)

P (r = 3) = 0.19537

=> at r = 4

P (r = 4) = [100,000! / (100,000 – 4)! 4!] (0.00004)^4 * (0.99996)^(100,000 – 4)

P (r = 4) = 0.19537

=> at r = 5

P (r = 5) = [100,000! / (100,000 – 5)! 5!] (0.00004)^5 * (0.99996)^(100,000 – 5)

P (r = 5) = 0.15630

=> at r = 6

P (r = 6) = [100,000! / (100,000 – 6)! 6!] (0.00004)^6 * (0.99996)^(100,000 – 6)

P (r = 6) = 0.10420

So the total P is:

P (r = 0 to 6) = 0.01831 + 0.07326 + 0.14652 + 0.19537 + 0.19537 + 0.15630 + 0.10420

P (r = 0 to 6) = 0.88933

=> So the probability that 7 or more people will have the disease is:

P (r ≥ 7) = 1 - 0.88933

P (r ≥ 7) = 0.11067 = 11.067%

There is only 0.11067 or 11.067% probability that 7 or more will have the disorder.

To solve this problem, we can use the binomial probability formula. The probability of exactly x successes in n trials is given by the formula. In this case, the probability of success (p) is 0.00004, and the total number of trials (n) is 100,000. To find the probability that seven or more people will have the rare blood disorder, we need to calculate the sum of the probabilities for x = 7, 8, 9, ..., 100,000.

To solve this problem, we can use the binomial probability formula. The probability of exactly x successes in n trials is given by the formula:

P(x) = C(n, x) * p^x * (1 - p)^(n - x)

where:

P(x) is the probability of x successes

C(n, x) is the number of combinations of n trials and x successes

p is the probability of success in a single trial

n is the total number of trials

In this case, the probability of success (p) is 0.00004, and the total number of trials (n) is 100,000.

To find the probability that seven or more people will have the rare blood disorder, we need to calculate the sum of the probabilities for x = 7, 8, 9, ..., 100,000. This can be done using the binomial probability formula or statistical tables.

To solve this problem, we use the binomial probability equation.

P = [n! / (n – r)! r!] p^r q^(n – r)

where,

n is the total number of samples = 6

r is the number of defective = 4

p is the probability it will be defective = 0.10

q is the probability it wont be = 0.90

P = [6! / (6 – 4)! 4!] (0.10)^4 * (0.90)^(6 – 4)

P = 1.215 x 10^-3 = 0.1215%

the probability that the average cost of nonsmoking rooms with a king-sized bed from 15 hotels in the area will be more than $150 is approximately 0.0081, or 0.81%.

To find the probability that the average cost of nonsmoking rooms with a king-sized bed from 15 hotels will be more than $150, we can use the Central Limit Theorem. Here's how:

1. Calculate the standard error of the mean (SEM) which is the standard deviation of the sample mean:

SEM = standard deviation / sqrt(sample size)

SEM = $29.12 / sqrt(15) ≈ $7.52

2. Calculate the z-score for a mean of $150:

z = (sample mean - population mean) / SEM

z = ($150 - $131.80) / $7.52 ≈ 2.41

3. Look up the z-score in the standard normal distribution table to find the probability associated with this z-score. The area to the right of a z-score of 2.41 gives us the probability that the average cost will be more than $150.

4. From the standard normal distribution table, a z-score of 2.41 corresponds to a probability of approximately 0.0081.

Therefore, the probability that the average cost of nonsmoking rooms with a king-sized bed from 15 hotels in the area will be more than $150 is approximately 0.0081, or 0.81%.

Using the map scale of 1cm equals 18 miles, the actual length of Clay's vacation route is calculated as 252 miles by multiplying 14 centimeters (the length on the map) by 18 miles (the scale conversion factor).

Clay is using a map scale to plan his vacation route. The scale of the map is given as 1cm equals 18 miles. To calculate the actual length of Clay's vacation route in miles, we can set up a simple proportion. Since 1cm on the map represents 18 miles in reality, we multiply the length on the map, which is 14 centimeters, by 18 to find out how many miles this length represents:

Length in miles = 14 cm * 18 miles/cm

After performing the multiplication, we get:

Length in miles = 252 miles

Therefore, Clay’s vacation route is 252 miles long according to the map's scale.

Given

Yeastie boys new album bread and the bank goes on sale next week

They autographed 85% of 2000 copies

Find out  how many albums were autographed.

To proof

Total copies = 2000

autographed 85% of 2000 copies

First convert 85% in decimal form

= [tex]\frac{85}{100}[/tex]

= 0.85

Now find out 85% 0f 20000

= 0.85 × 2000

= 1700

The albums autographed were 1700.

Hence proved

Final answer:

To find the opposite of the expression [tex]-8c^3-10c^2+6c+5[/tex], change the sign of each term to get  [tex]8c^3+10c^2-6c-5.[/tex].

Explanation:

The opposite of any algebraic expression is found by changing the sign of each term within the expression. To find the opposite of the expression  [tex]-8c^3-10c^2+6c+5[/tex], simply change the signs of each term:

Putting it all together, the opposite of the expression  [tex]-8c^3-10c^2+6c+5[/tex] is [tex]8c^3+10c^2-6c-5.[/tex]

In essence, each term in the original expression is multiplied by -1 to obtain its opposite. This operation changes all positive terms to negative and all negative terms to positive.

The concept of taking the opposite is fundamental in algebra and is often used in simplifying expressions, solving equations, and manipulating mathematical statements.

Answer:

x = 45°

Step-by-step explanation:

It a transversal line intersect two parallel lines, then alternative interior angles are congruent.

From the below graph it is clear that the line m and n are two parallel lines and l is a transversal line.

[tex]\angle ABC\cong \angle BCD[/tex]          (Alternative interior angles)

[tex]m\angle ABC=m\angle BCD[/tex]          (Definition of congruent angles)

[tex]x+30^{\circ}=75^{\circ}[/tex]

Subtract 30° from both sides.

[tex]x+30^{\circ}-30^{\circ}=75^{\circ}-30^{\circ}[/tex]

[tex]x=45^{\circ}[/tex]

Therefore the measure of angle x is 45°.

Answer:

UDP- User Datagram protocol (UDP), is a part of internet protocol suite. It is basically present on the Transport layer of the "Internet Network Model"

Step-by-step explanation:

As the Transport layer  of the model, the UDP, SCTP and TCP's are present. Now originally in the TCP/IP model there are four layers:

The correct layer of the OSI model that is most directly impacted when an internet service provider (ISP) is found to be blocking UDP traffic from a source host is the Transport Layer.

The OSI model consists of seven layers, with the Transport Layer being the fourth layer. This layer is responsible for providing communication services directly to the application processes running on different hosts. The Transport Layer is where protocols like TCP (Transmission Control Protocol) and UDP (User Datagram Protocol) operate.

UDP (User Datagram Protocol) is a transport layer protocol that is used for sending messages (datagrams) in an internet protocol network. It is an alternative to the TCP protocol and is known for its simplicity and efficiency, particularly in cases where error checking and ordering are not necessary.

When an ISP blocks UDP traffic, it is directly interfering with the way the Transport Layer functions for applications that rely on UDP for data transmission. This action prevents UDP packets from being delivered to the intended destination, which can affect applications and services that use UDP for real-time data transmission, such as VoIP (Voice over Internet Protocol), online gaming, and streaming services.

The other layers of the OSI model are not directly impacted by the blocking of UDP traffic:

1. Physical Layer: Deals with the transmission and reception of the unstructured raw bit stream over a physical medium.

2. Data Link Layer: Responsible for node-to-node data transfer and error detection and handling.

3. Network Layer: Manages device addressing, tracks the location of devices on the network, and determines the best way to move data.

4. Transport Layer: Provides transparent transfer of data between end systems, or hosts, and is responsible for end-to-end error recovery and flow control.

5. Session Layer: Manages sessions between end-users, i.e., the opening, closing, and management of sessions between end-user applications.

6. Presentation Layer: Transforms data to provide a standard interface for the Application Layer. It is responsible for data encryption and decryption, as well as data compression.

7. Application Layer: Provides network services to the applications of the user, such as email, file transfer, and web browsing.

Since UDP operates at the Transport Layer, this is the layer most directly impacted by the ISP's decision to block UDP traffic.

Answer:

[tex]5^2+2[73-(4\times 5)]=131[/tex]                  

Step-by-step explanation:

Given : Expression [tex]5^2+2[73-(4\times 5)][/tex]

To find : What is the solution of the expression ?

Solution :

Expression [tex]5^2+2[73-(4\times 5)][/tex]

Applying BODMAS,

We multiply the term,

[tex]=5^2+2[73-(20)][/tex]

Solve the bracket by subtraction,

[tex]=5^2+2[53][/tex]

Open the bracket and solve quadratic,

[tex]=25+106[/tex]

Add the terms,

[tex]=131[/tex]

Therefore, [tex]5^2+2[73-(4\times 5)]=131[/tex]

The value of 3 in the number 18.35 is in the tenths place, representing three tenths or 0.3.

The value of 3 in 18.35 is in the tenths place, which means it represents three tenths or 0.3 in decimal form. To understand the place value of digits in a decimal number, one must be aware that each position to the right of the decimal point indicates a fractional part of 10. In the number 18.35, the digit 3 is in the tenths place, the 5 is in the hundredths place, and the 1 and the 8 are in the ones and tens places, respectively, to the left of the decimal point.

The value of 3 in 18.35 is 0.03. When looking at a decimal number, each digit occupies a place value. The value of 3 in 18.35 is in the hundredths place. It represents 3 hundredths or 0.03.

Answer:

Part 1) The constant of variation is [tex]k=1/9[/tex]

part 2) The equation is [tex]y=\frac{1}{9}x[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

Let

x -----> the number of square feet

y ----->  the number of square yards

Three square yards are equivalent to 27 square feet

so

we have the point (27,3)

Part 1) What is the constant of variation?

The constant of variation or proportionality is equal to

[tex]k=y/x[/tex]

substitute the values

[tex]k=3/27[/tex]

Simplify

[tex]k=1/9[/tex]

Part 2) What is the equation representing the direct variation?

we know that

[tex]y=kx[/tex]

substitute the value of k

[tex]y=\frac{1}{9}x[/tex]

This equation shows that the number of square yards (y) is directly proportional to the number of square feet (x) with a constant of variation equal to 1/9.

In direct variation, the relationship between two variables can be represented by the formula:

y = kx

Where:

- y represents one variable (in this case, the number of square yards).

- x represents the other variable (in this case, the number of square feet).

- k is the constant of variation, which remains the same for all data points in the direct variation.

In this specific case, you've mentioned that 3 square yards are equivalent to 27 square feet. You can use this information to find the constant of variation (k). You can choose one of the data points to solve for k. Let's use the point (3, 27):

3 = k * 27

Now, solve for k:

k = 3 / 27

k = 1 / 9

So, the constant of variation (k) is 1/9. The equation representing the direct variation is:

y = (1/9)x

This equation shows that the number of square yards (y) is directly proportional to the number of square feet (x) with a constant of variation equal to 1/9.

Learn more about proportionality here

https://brainly.com/question/15065328

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looks like the numbers doubles in the problem

 shouldn't it be 5 girls to 4 boys in a class total of 27??

5+4 =9

27/9=3

5*3 = 15

there are 15 girls in class