Define a sample space and count the number of sample points in the sample space for each of the following experiments. a. Select at random a set of 5 questions from a set of 15 questions. b. Form by random selection a committee of 5 from a membership of 20.

Answers

Answer 1

There are 15C5 or 3003 possible combinations in the sample space.There are 20C5 or 15504 possible combinations in the sample space.

What is number?

A number is a mathematical object used to count, measure, and label. Numbers can be represented in many different forms such as natural numbers, integers, real numbers, and complex numbers. They can also be classified as scalar numbers (which have a magnitude or value only) or vector numbers (which have both magnitude and direction). Numbers can be used to represent many different things, including measurements, distances, money, and quantities.

A) Sample Space: The sample space for selecting a set of 5 questions from a set of 15 questions is the set of all possible combinations of 5 questions from 15 questions. There are 15C5 or 3003 possible combinations in the sample space.

B) Sample Space: The sample space for forming a committee of 5 from a membership of 20 is the set of all possible committees that can be formed from 20 members. There are 20C5 or 15504 possible combinations in the sample space.

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Answer 2

The original price of the pearl was 52 euros.

What is price?

Price is the monetary value of a product, service, or asset. It is one of the most important factors in a customer's decision to purchase something. Price also determines the amount of profit a business makes on a particular product or service. Price is a key component of the marketing mix, and it can be used to create a sense of value for customers. Price can also be used to differentiate a product from competitors, as well as to indicate quality levels and to create loyalty.

a) One of the cheapest pearls costs 41 euros.

b) This necklace costs 2153 euros, which is the sum of all the pearls.

c) The pearl with the crack originally cost 52 euros. The price was reduced by 1/5, which is 10.4 euros, making the price of the pearl 41.6 euros. The decrease in price of the necklace was 6.5 euros, which means the reduction in price of the pearl was 6.5 euros. Therefore, the original price of the pearl was 52 euros.

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Related Questions

8x<168
The solution of the inequality is

Answers

Answer:

8×21=168? That would make it 168=168? Or you could multiply even more to make 8×25 or somethin?

Step-by-step explanation: I don't know what answer ur looking for but there's some help

Answer:

x < 21.

Step-by-step explanation:

Given the equation: 8x < 168, solve the inequality.

First, make it as if it was an equality and solve x:

8x = 168  (Divide both sides by 8)

x = 21

That means x < 21.

Determine if the ordered pair (-2, -4) is a solution for equation 2y - 3x = -2.

Answers

Answer:

Step-by-step explanation:

2(-4) - 3(-2) = -2

 -8 + 6 = -2

   -2 = -2

Write the following series in sigma notation. 2 + 12 + 22 + 32 + 42

Answers

The given series in the sigma notation can be written as [tex]\sum_{n = 1} ^ 5 10n - 8[/tex].

What are arithmetic series?

An arithmetic series is a set of integers where each term is made up of the common difference, a fixed amount, and the sum of the terms before it. In other words, the terms of the series may be represented as follows if the first term of an arithmetic series is a and the common difference is d:

a, a + d, a + 2d, a + 3d, ...

The given series is 2 + 12 + 22 + 32 + 42.

The total number of terms are 5.

The first term is 2, and the common difference is:

d = 12 - 2 = 10

Now, using the nth term of sequence we have:

an = 2 + (n - 1) 10

= 10n - 8

= [tex]\sum_{n = 1} ^ 5 10n - 8[/tex]

Hence, the given series in the sigma notation can be written as [tex]\sum_{n = 1} ^ 5 10n - 8[/tex].

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You are playing a game with a friend. It costs you $2 to play. If you roll a 1 on a 6-sided die you win $4. If you roll a 2, 3, 4, 5, or 6 you win nothing and lose $2 the cost to play. How much should the player be willing to pay to play this game and not lose money in the long run?

Answers

The player should be willing to pay up to $1.33 to play this game and not lose money in the long run.

The expected value is the sum of the products of each possible outcome and its probability. Let's calculate the expected value of the game:

E(X) = (1/6) * $4 + (5/6) * (-$2)

E(X) = $0.67

This means that on average, the player can expect to win $0.67 per game. Since it costs $2 to play, the player should not be willing to pay more than $2 - $0.67 = $1.33 to play the game and not lose money in the long run.

Probability theory is based on axioms, which are basic assumptions about the nature of probability. It is used to quantify uncertainty and to make predictions based on the available information. Probability is expressed as a number between 0 and 1, with 0 meaning an event is impossible, and 1 meaning an event is certain.

The concept of probability is used in a variety of fields, including statistics, economics, engineering, and physics. In statistics, probability is used to model random variables, estimate parameters, and test hypotheses. In economics, probability is used to model financial risks and decision-making under uncertainty. In engineering and physics, probability is used to model complex systems and predict the behavior of particles.

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A dairy made 98.38 ounces of yogurt. Then a local market bought 86.2 ounces of the yogurt.
How much yogurt does the dairy have left?

Answers

The amount of yoghurt left is 12. 18 ounces

How to determine the number

The algebraic expressions are defined as those expressions that are made up of variables, terms, constants, factors and coefficients.

The expressions are also composed of some arithmetic or mathematical operations, such as;

BracketParenthesesDivisionAdditionSubtractionMultiplication

From the information given,

Let the total number of ounces of yoghurt be x

Let the number of ounces of yoghurt sold be y

We have that;

The number left= x - y

= 98.38 - 86.2

= 12. 18 ounces of yoghurt

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please help fast I am baffled

Answers

The expression for the number of non-adult sizes is s - 19.

What are expressions?

A value or amount is represented by an expression, which is a collection of numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division. Calculations, complicated mathematical equations, and issues in a variety of disciplines, including science, engineering, economics, and statistics, may all be solved using expressions. Functions that depict a connection between variables, such as sin(x) and log(x), can also be included in expressions. Expressions are frequently employed to simulate real-world circumstances and provide predictions based on mathematical analysis.

Given that the total number od sweatshirts = s.

The number of non-adult sweatshirts can be calculated by:

Number of non-adult sizes = Total number of sweatshirts sold - Number of adult sizes

= s - 19

Hence, the expression for the number of non-adult sizes is s - 19.

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Please urgent need the work and answer
X=3.2
Y=6.1
Z=0.2

XZ +Y2

Answers

Answer: 37.85

Step-by-step explanation:

Substitute: 3.2x0.2+6.1^2

Calculate the product or quotient: 0.64+6.1^2

Calculate the power: 0.64+37.21

Calculate the sum or difference: 37.85

Answer:  37.85

pls mark brainliest

A triangle has two sides of length 3 and 16. What is the largest possible whole-number length for the third side

Answers

The largest possible whole-number length for the third side is 18, which satisfies all three inequalities.

What is inequality theorem?

The triangle inequality theorem explains the relationship between the three sides of a triangle. This theorem states that for any triangle, the sum of the lengths of the first two sides is always larger than the length of the third side.

According to question:

Let x be the length of the third side. By the triangle inequality, we have:

3 + 16 > x and 16 + x > 3 and 3 + x > 16

Simplifying, we get:

19 > x and x > 13 and x < 19

The largest possible whole-number length for the third side is 18, which satisfies all three inequalities.

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Jim orders prints from a website. The site charges him $6. 95 a month and $0. 04 for each print he orders.

Enter an equation that can be used to find the number of prints, P, Jim ordered last month if the website charged

him $17. 79. Enter your response in the first response box

Enter the number of prints Jim ordered last month. Enter your response in the second response box,

Answers

Number of  prints Jim ordered last month is 271

Let's assume Jim ordered "P" prints last month. The cost of ordering "P" prints would be the sum of the monthly charge and the cost of each print, which is given by the equation:

Cost = Monthly Charge + (Cost per Print x Number of Prints)

Substitute the values in the equation

$17.79 = $6.95 + ($0.04 x P)

Simplifying the equation, we get:

$10.84 = $0.04 x P

Dividing both sides by $0.04, we get:

P = $10.84 / $0.04

Divide the numbers

P = 271

Therefore, Jim ordered 271 prints last month.

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To train for a race, Rosmaria runs 1.5 hours longer each week than she did the previous week. In the first week, Rosmaria ran 3
hours. How much time will Rosmaria spend running if she trains for 12 weeks?

first to answer with good explanation gets brainlest

Answers

In linear equation, 54 hours time will Rosmaria spend running if she trains for 12 week.

What is a linear equation in math?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Rosmaria runs 1.5 hours.

In the first week, Rosmaria ran 3 hours.

Rosmaria spend running if she trains for 12 weeks = 12 * 1.5 * 3

                                                             = 54

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What x-values are a solution to the System?

Select EACH correct answer.

Question 2 options:

x = -2


x = -1


x = 0


x = 1


x = 2

Answers

The solutions to the system equations are x = -1 and x = 0.

What is a system of equations?

When two or more variables are related to one another and equations are constructed to determine each variable's value, the result is a system of equations. an equation is a balance scale, and for the equation to stay true, both sides must be equal.

Given equations are:

[tex]y=2^x - 1\\y=\frac{1}{2} x[/tex]

The solutions of the system for which; [tex]y_{1} =y_{2}[/tex]

According to the given table, the solutions to the system of both equations at x = -1 and x = 0.

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What is the value of 3x + 6 if x = -5

Answers

Answer:

-9

Step-by-step explanation:

x = -5

3x + 6

Since x = -5..

Do this

3(-5) + 6

Perform

-15 + 6

Answer: -9

Therefore, when x is equal to -5, the value of 3x + 6 is -9.

What is equation?

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

3x + 6 = 3(-5) + 6

= -15 + 6

= -9

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If the ratio a: b is 1 : 4 and the ratio b: c= 3:2, find the ratio (a + c) : c.

Answers

The required ratio of  is (a + c) : c 11:8.

How to find ratio ?

Given that a:b=1:4 and b:c=3:2.

We can simplify the ratio b:c by multiplying both sides by 4 to get b:c=12:8=3:2.

To find the ratio (a+c):c, we need to express a and c in terms of b. From the first ratio, we have [tex]a=\frac14 b$[/tex]. From the second ratio, we have [tex]c=\frac{2}{3}b$[/tex]. Substituting these values into the expression (a+c):c, we get:

[tex]$$(a+c):c = \left(\frac{1}{4}b + \frac{2}{3}b\right):\frac{2}{3}b$$[/tex]

Simplifying the expression inside the parentheses, we get:

[tex]$\frac{1}{4}b + \frac{2}{3}b = \frac{3b}{12} + \frac{8b}{12} = \frac{11b}{12}$$[/tex]

Therefore, the ratio [tex]$(a+c):c$[/tex] is:

[tex]$(a+c):c = \frac{11b}{12}:\frac{2}{3}b = 11:8$$[/tex]

Hence, the required ratio is 11:8$.

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HELP DUE TODAY!!!!!!!!!
. Write the (x, y) coordinates for P in terms of cosine and sin.
6. Using the image above, if cos(Θ) = 0.6, what are the coordinates of P? Explain your reasoning.

Answers

Answer:   (0.6,  -0.8)

Explanation:

Use the pythagorean trig identity to determine sine based on cos(theta) = 0.6

[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\sin^2(\theta)=1-\cos^2(\theta)\\\\\sin(\theta)=\pm\sqrt{1-\cos^2(\theta)}\\\\\sin(\theta)=-\sqrt{1-\cos^2(\theta)} \ \ \text{....sine is negative in quadrant Q4}\\\\\sin(\theta)=-\sqrt{1-(0.6)^2}\\\\\sin(\theta)=-\sqrt{1-0.36}\\\\\sin(\theta)=-\sqrt{0.64}\\\\\sin(\theta)=-0.8\\\\[/tex]

Since [tex]\cos(\theta)=0.6 \text{ and } \sin(\theta)=-0.8[/tex], the location of point P is (0.6, -0.8)

Recall that for any point (x,y) on the unit circle, we have:

[tex]\text{x}=\cos(\theta)\\\\\text{y}=\sin(\theta)[/tex]

meaning cosine is listed first in any (x,y) pairing.

find the inverse of the function

F(x) = x² + 2x₁ [-1, 00]

Answers

To find the inverse of the function F(x) = x² + 2x over the interval [-1, 0], we need to follow these steps:

1. Replace F(x) with y to get y = x² + 2x.
2. Rearrange the equation to isolate x: y = x² + 2x becomes x² + 2x - y = 0.
3. Use the quadratic formula to solve for x in terms of y:

x = (-2 ± sqrt(4 + 4y)) / 2
x = -1 ± sqrt(1 + y)

4. Since the domain of F(x) is [-1, 0], we only consider the negative square root in the expression for x:

x = -1 - sqrt(1 + y)

5. Replace x with its inverse function notation, denoted by F^(-1)(y):

F^(-1)(y) = -1 - sqrt(1 + y)

Therefore, the inverse of the function F(x) = x² + 2x over the interval [-1, 0] is given by F^(-1)(y) = -1 - sqrt(1 + y).

You roll a fair 666-sided die. What is \text{P(roll greater than 4})P(roll greater than 4)start text, P, left parenthesis, r, o, l, l, space, g, r, e, a, t, e, r, space, t, h, a, n, space, 4, end text, right parenthesis?

Answers

When a 666-sided fair die is rolled, then the probability of rolling greater than 4 is  0.9940 or 99.40%.

Given that the die is fair and has 666 sides. So, each face of the die will have a probability of 1/666, i.e.,

p(1) = p(2) = ... = p(666) = 1/666.

The probability of rolling greater than 4 is P(roll greater than 4), which is the sum of the probabilities of rolling a 5, 6, 7, 8, 9, ..., 666. So,

P(roll greater than 4) = p(5) + p(6) + p(7) + ... + p(666)

P(roll greater than 4) = (1/666) + (1/666) + (1/666) + ... + (1/666)

(There are 661 terms)P(roll greater than 4) = 661(1/666)

P(roll greater than 4) = 0.9940 (rounded to four decimal places)

Hence, the probability of rolling greater than 4 is 0.9940 or 99.40%.

Alternatively, the probability of rolling greater than 4 is

   1 - P(roll less than or equal to 4)P(roll greater than 4)

= 1 - P(roll less than or equal to 4)P(roll greater than 4)

= 1 - (p(1) + p(2) + p(3) + p(4))P(roll greater than 4)

= 1 - (4/666)P(roll greater than 4)

= 1 - 0.0060P(roll greater than 4)

 = 0.9940 (rounded to four decimal places)

Hence, the probability of rolling greater than 4 is 0.9940 or 99.40%.

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Write an equation for the line on a graph below.

Answers

Check the picture below.

Answer:

x=-3

Step-by-step explanation:

what percentage of the area under the normal curve falls between ±2 standard deviations?

Answers

Approximately 95.44% of the data falls within ±2 standard deviations of the mean in a normal distribution.

How  the 95.44% of the area under the normal curve falls between ±2 standard deviations?

To find the percentage of the area under the normal curve that falls between ±2 standard deviations, we need to follow the following steps:

We need to know the mean (μ) and standard deviation (σ) of the normal distribution in question. If we assume a standard normal distribution (i.e., a normal distribution with mean of 0 and standard deviation of 1), then we can use a z-score table to find the percentage of area under the curve.

Calculate the z-scores for ±2 standard deviations

The z-score formula is:

z = (x - μ) / σ

For ±2 standard deviations, the values of x are μ ± 2σ. Therefore, the z-scores are:

z = (μ + 2σ - μ) / σ = 2

z = (μ - 2σ - μ) / σ = -2

Use a z-score table to find the percentage of area under the curve

A z-score table gives the percentage of area under the standard normal curve that falls to the left of a given z-score. Since the normal distribution is symmetric, the percentage of area to the right of a negative z-score is the same as the percentage of area to the left of the corresponding positive z-score.

Using a z-score table, we find that the percentage of area under the standard normal curve that falls to the left of z = 2 is 0.9772, or 97.72%. Therefore, the percentage of area under the curve that falls between ±2 standard deviations is:

97.72% - (100% - 97.72%) = 95.44%

This means that approximately 95.44% of the data falls within ±2 standard deviations of the mean in a normal distribution.

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Your teacher prepares a large container full of colored

beads. She claims that 1/8 of the beads are red, 1/4 are

blue, and the remainder are yellow. Your class will take a

simple random sample of beads from the container to test the teacher's claim. The smallest number of beads you

can take so that the conditions for performing inference

are met is.

15

16

30

40

90

Answers

The smallest number of beads we can take so that the conditions for performing inference are met is 40.

Probability:

The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probability of two complementary events A and B - A occurring or B occurring - adds up to 1.

According to the Question:

Given in the question,

Teacher prepares a large container filled with colored beads. She claims that 1/8 beads are red, 1/4are blue, and the rest are yellow. Your class will test the teacher's claim by randomly drawing a simple sample of beads from the container.

Quadrant                     Frequency

      1                                    18

      2                                   22

      3                                   39

      4                                   21

The proportions are 1/8 , 1/4 and 5/8

Here, the smallest probability is 1/8 , thus it would be used to compute the frequency.

Now,

The expected frequencies are calculated as:

E = np₁ = 15 (1/8) = 1.875

E = np₂ = 16(1/8) = 2

E = np₃ = 30(1/8) = 3.75

E = np₄ = 40(1/8) = 5

E = np₅ = 80(1/8) = 10

Here, conditions are fulfilling for 40 and 90 but the smallest sample size is contained by 40. Thus, the correct option is 40.

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Xavier buys a dog collar that costs $6.79. He pays for the dog collar
with a $10 bill.
How much change does Xavier receive?

Answers

Answer: Xavier will receive $3.21 in change.

Step-by-step explanation:

To find the change Xavier receives, we need to subtract the cost of the dog collar from the amount he paid with his $10 bill:

Change = $10 - $6.79 = $3.21

Therefore, Xavier will receive $3.21 in change.

b) There are x number of books that worth Rs. 35 each and 5 books worth Rs. 30 each in a parcel prepared as a gift. The value of two such parcels is Rs. 580. i. Build up an equation using the above information. ii. Find the value of x by solving the equation.​

Answers

Answer:

Equation: 2(357+30×5) = 580

x=4

Step-by-step explanation:

In one package, there is such a relationship:

357+30X5 = y

(Y is the price of a package)

The price of two parcels is 580:

then. 24=580

y= 290

x=4, so: equation: 2(35x+150) =580

Step-by-step explanation:

A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more for the same amount each book would have cost Rs. 1 less. How many books did he buy?

A

8

B

16

Correct Answer

C

24

D

28

Medium

Open in App

Updated on : 2022-09-05

Solution

Verified by Toppr

Correct option is B)

Let the shopkeeper buy x number of books. 

According to the given condition cost of x books =Rs80

Therefore cost of each book =x80

Again when he had brought 4 more books

Then total books in this case =x+4

So cost of each book in this case =x+480

According to Question, 

x80−x+480=1

x(x+4)80(x+4)−80x=1

x2+20x−16x−320=0

(x−16)(x+20)=0

x=16orx=−20

Hence the shopkeeper brought 16 books

i have a small area that i want to place 2 bench press machines. how much room will i need to reserve for those?

Answers

To place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet. Let's discuss it in detail below. Here are the dimensions of the bench press machine, which can help determine the amount of space required to fit two bench press machines in a small area:

The length of the bench press machine is between 48 inches and 54 inches.

The width of the bench press machine is between 28 inches and 32 inches.

The height of the bench press machine is between 48 inches and 56 inches.

Based on the above dimensions of the bench press machine, two machines can be placed in a small area of 10 feet by 10 feet. However, for safe use, the following guidelines should be followed:

There should be at least 6 feet of distance between the two bench press machines. There should be at least 3 feet of clearance in the front of the bench press machine to allow for safe movement during exercises. There should be at least 2 feet of clearance behind the bench press machine to allow for a safe exit in case of an emergency.

Thus, to place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet.

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tomas has $1,000 to spend on a vacation. his plane ticket costs $348.25. if he stays 5.5 days at his destination, how much can he spend each day? write an inequality and then solve.

Answers

Tomas can spend at most $118.50 each day. The inequality equation is 5.5x ≤ 651.75.

Tomas has $1,000 to spend on a vacation. His plane ticket costs $348.25. If he stays 5.5 days at his destination, how much can he spend each day? Write an inequality and then solve.

Let x be the amount that Tomas can spend each day. Since Tomas has to pay for the plane ticket, he will have $1,000 − $348.25 = $651.75 left to spend on the rest of the vacation.

Then, since he is staying for 5.5 days, the total amount he can spend would be 5.5x dollars. The inequality that represents the problem is as follows:

5.5x ≤ 651.75

To solve for x, divide both sides by 5.5

5.5x/5.5 ≤ 651.75/5.5x ≤ 118.5

Therefore, Tomas can spend at most $118.50 each day.

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Answer:

The answer to this solution is 118.5 a day

Step-by-step explanation:

The original price is $1,000 for the ticket it costs $348.25 and Tomas is staying for 5.5 days so dividing 651.75 by 5.5 is the ANSWER 118.5

Write the first four terms of the sequence defined by a n = 5
{5, if n=1
a n -1 -5, if n>1

Answers

Answer:

The sequence is defined as follows:

a1 = 5

an = an-1 - 5, for n > 1

Using this definition, we can find the first four terms of the sequence as follows:

a1 = 5

a2 = a1 - 5 = 5 - 5 = 0

a3 = a2 - 5 = 0 - 5 = -5

a4 = a3 - 5 = -5 - 5 = -10

Therefore, the first four terms of the sequence are: 5, 0, -5, -10.

consider the ordered bases and for the vector space of lower triangular matrices with zero trace. a. find the transition matrix from to . hint: use the standard basis . b. find the coordinates of in the ordered basis if the coordinate vector of in is . c. find .

Answers

a. Finding the transition matrix from B1 to B2 using the standard basis for the vector space of lower triangular matrices with zero trace.The standard basis of the vector space of lower triangular matrices with zero trace is given by{(1,0,0),(0,1,0),(0,0,0)}.We are to find the transition matrix from B1 to B2. We start with the definition of the transition matrix. This definition states that if A = [a1,a2,a3] is a matrix whose columns are the vectors of B2, then the transition matrix from B1 to B2 is the matrix S such that S = [b1,b2,b3] where bi is the column vector obtained by expressing the ith vector of B1 as a linear combination of the vectors of B2. Using the standard basis, we have that (1,0,0) = a1, (0,1,0) = a2 and (0,0,0) = a3. Therefore, we need to express each of these standard basis vectors as a linear combination of the vectors of B1.For (1,0,0), we have(1,0,0) = 2e1 - e2For (0,1,0), we have(0,1,0) = -3e1 + e3For (0,0,0), we have(0,0,0) = e2 + e3Therefore, the transition matrix S is given by S = [b1,b2,b3] where bi is obtained by expressing the ith vector of the standard basis as a linear combination of the vectors of B1. Thus,S = [(2,-3,0),(-1,1,0),(0,0,1)]b. Finding the coordinates of v in B if the coordinate vector of v in B1 is c. Let c be the coordinate vector of v with respect to B1. Then we know that v = c1e1 + c2e2 + c3e3. We are to find the coordinate vector of v with respect to B.We know that B is a basis for the vector space of lower triangular matrices with zero trace, so any vector in this space can be expressed uniquely as a linear combination of the vectors in B. Thus, we can write v as a linear combination of the vectors of B.v = a1x1 + a2x2 + a3x3We are to find the coefficients x1, x2 and x3. We do this by using the fact that the transition matrix S from B1 to B is such that v = Sc where c is the coordinate vector of v with respect to B1. Hence, v = Sc = [b1,b2,b3][c1,c2,c3] = (2c1 - c2) b1 - (c1 - c2) b2 + c3 b3Using the expressions for b1, b2 and b3 in terms of the standard basis vectors, we obtainv = (2c1 - c2)(2e1 - e2) - (c1 - c2)(-e1 + e3) + c3e3

Expanding this expression and comparing coefficients with the equation for v above yields(2c1 - c2)(2e1 - e2) - (c1 - c2)(-e1 + e3) + c3e3 = c1e1 + c2e2 + c3e3Therefore, we have the system of equations2(2c1 - c2) - (c1 - c2) = c11(2c1 - c2) + (c1 - c2) = c20 = c3Solving for x1, x2 and x3 yieldsx1 = c2/2, x2 = c1/2, and x3 = 0Therefore, the coordinate vector of v with respect to B is given by the vector( c2/2, c1/2, 0).c. Finding [v]B2 in 200 wordsWe are to find the coordinate vector of v with respect to B2. Since we already have the coordinate vector of v with respect to B1, we can use the transition matrix S from B1 to B2 to obtain this coordinate vector.Let c be the coordinate vector of v with respect to B1. Then, we know that v = c1e1 + c2e2 + c3e3. Since the coordinate vector of v with respect to B1 is c, we have the equationc = [c1,c2,c3]Using the transition matrix S from B1 to B2, we can write the coordinate vector of v with respect to B2 as[x1,x2,x3] = S[c1,c2,c3]Multiplying these matrices together yields the equation[x1,x2,x3] = [(2,-3,0),(-1,1,0),(0,0,1)][c1,c2,c3]

Expanding this equation gives the system of equations2c1 - c2 = x1-3c1 + c2 = x2c3 = x3Solving this system of equations for c1, c2 and c3 yieldsc1 = (x2 - x1)/4, c2 = (3x2 + x1)/4, and c3 = x3Therefore, the coordinate vector of v with respect to B2 is given by the vector((x2 - x1)/4, (3x2 + x1)/4, x3).

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Find the measure of the last angle of the triangle below.
28⁰
35°

Answers

Measure of last angle of triangle is 117°

Triangle Properties

The triangle's characteristics include:

All triangles have a total of 180 degrees in their angles.The length of the longest two sides of a triangle is greater than the length of the third side.The length of the third side of a triangle is shorter than the difference between its two sides.Angle Sum Property

The angle sum property states that the sum of a triangle's three interior angles is always 180 degrees.

Angle of Triangle are

28° and 35°

Let the third angle be x

According to angle sum property

28°+35°+x=180°

x=117°

Measure of last angle of triangle is 117°

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The complete question is;

Find the measure of the last angle of the triangle below.

28⁰

35°

Image is attached below.

Write 735 as the product of its prime factor.

Answers

Answer:

[tex]735 = 3 \times 5 \times {7}^{2} [/tex]

Step-by-step explanation:

[tex]735 = 7 \times 105[/tex]

[tex]735 = 7 \times 3 \times 35[/tex]

[tex]735 = 7 \times 3 \times 5 \times 7[/tex]

[tex]735 = 3 \times 5 \times {7}^{2} [/tex]

Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree.

Answers

Answer:

Were sorry! Answer is not available right now check in later.

Step-by-step explanation:

She begins at sea level, which is an elevation of 0 feet.
She descends for 50 seconds at a speed of 5 feet per second.
She then ascends for 54 seconds at a speed of 4.4 feet per second.

Answers

Answer:

The diver descends:

50 seconds x 5 feet/second = 250 feet

The diver ascends:

54 seconds x 4.4 feet/second = 237.6 feet

Therefore, the total change in elevation is:

250 feet (descent) - 237.6 feet (ascent) = 12.4 feet

So, the diver's final elevation is:

0 feet (starting elevation) - 12.4 feet (change in elevation) = -12.4 feet

Therefore, the diver ends up 12.4 feet below sea level.

Answer:

it is 1

Step-by-step explanation:

its is 1 2 3 hsvs jafsnsjhd jsusgsmsi jshsbjdg

For each growth rate, find the associated growth factor.
1. 30% increase
2. 30% decrease
3. 2% increase
4. 2% decrease
5. 0.04% increase
6. 0.04% decrease
7. 100% increase

Answers

Answer:

The associated growth factor for a 30% increase is 1 + 0.30 = 1.30.

The associated growth factor for a 30% decrease is 1 - 0.30 = 0.70.

The associated growth factor for a 2% increase is 1 + 0.02 = 1.02.

The associated growth factor for a 2% decrease is 1 - 0.02 = 0.98.

The associated growth factor for a 0.04% increase is 1 + 0.0004 = 1.0004.

The associated growth factor for a 0.04% decrease is 1 - 0.0004 = 0.9996.

The associated growth factor for a 100% increase is 1 + 1 = 2.

Step-by-step explanation:

A growth factor is a multiplier that represents the amount by which a quantity changes as a result of a growth rate or percentage change. It is calculated by adding 1 to the decimal form of the growth rate. For example, if the growth rate is 30%, the decimal form is 0.30, and the growth factor is 1 + 0.30 = 1.30.

In case of a decrease, the growth factor is calculated by subtracting the decimal form of the decrease rate from 1. For example, if the decrease rate is 30%, the decimal form is 0.30, and the growth factor is 1 - 0.30 = 0.70.

In cases where the growth rate is a small percentage, it is important to convert it into a decimal by dividing the percentage by 100 before calculating the growth factor.

In the case of a 100% increase, the quantity doubles, so the growth factor is 2 (i.e., 1 + 1).

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