6u^2+17u-10
factor please

The process to show that if 16 people are seated in a row of 20 chairs, then some group of 4 consecutive chairs must be occupied is shown below.

We prove this using the Pigeonhole Principle, which states that if n items are placed into m containers, and n > m, then at least one container must contain more than one item.

Let us consider the 16 people seated in a row of 20 chairs. Each person occupies one chair, so there are 20 - 16 = 4 empty chairs in the row.

We assume that empty chairs as containers, and people as items that need to be placed into containers.

Since there are more items (people) than containers (empty chairs), there must be at least one group of 2 or more consecutive empty chairs.

Now, let's consider the complement of this statement: Suppose there are no groups of 4 consecutive chairs that are occupied. Then, each group of 4 consecutive chairs contains at most 3 people.

We partition the row of chairs into groups of 4 consecutive chairs.

So, there are 20 - 3 = 17 such groups. By the statement above, each of these groups contains at most 3 people. Therefore, the total number of people seated in the row is at most 17×3 = 51.

But, we know that there are actually 16 people seated in the row. This is a contradiction, since 51 < 16. Therefore, our assumption that there are no groups of 4 consecutive chairs that are occupied must be false, and we have proved that some group of 4 consecutive chairs must be occupied.

Learn more about Pigeonhole Principle here

https://brainly.com/question/30322724

#SPJ4

Answer:

1.11

2.4

3.5

pls correct me if I'm wrong

Answer:

38. (b) 11

39. (c) 4

40. (c) 5

Step-by-step explanation:

38.)

[tex]\implies \: \sf \sqrt{3xx - 8} = 5 \\ \\ \implies \: \sf 3xx - 8 = {(5)}^{2} \\ \\ \implies \: \sf 3xx - 8 = 25 \\ \\ \implies \: \sf 3xx = 25 + 8 \\ \\ \implies \: \sf 3xx = 33 \\ \\ \implies \: \sf xx = \dfrac{33}{3} \\ \\ \implies \: \sf xx = 11\\ [/tex]

Hence, Required answer is option (b) 11.

39.)

[tex]\implies \: \sf \sqrt{4xx -7 } - 3 = 0 \\ \\ \implies \: \sf \sqrt{4xx - 7} = 3 \\ \\ \implies \: \sf 4xx - 7 = {(3)}^{2} \\ \\ \implies \: \sf 4xx - 7 = 9 \\ \\ \implies \: \sf 4xx = 9 + 7 \\ \\ \implies \: \sf 4xx = 16 \\ \\ \implies \: \sf xx = \dfrac{16}{4} \\ \\ \implies \: \sf xx = 4 \\ [/tex]

Hence, Required answer is option (c) 4.

40.)

[tex]\implies \: \sf \sqrt{6xx + 6} - 6 = 0 \\ \\ \implies \: \sf \sqrt{6xx + 6} = 6 \\ \\ \implies \: \sf 6xx + 6 = {(6)}^{2} \\ \\ \implies \: \sf 6xx + 6 = 36 \\ \\ \implies \: \sf 6xx = 36 - 6 \\ \\ \implies \: \sf 6xx = 30 \\ \\ \implies \: \sf xx = \dfrac{30}{6} \\ \\ \implies \: \sf xx = 5 \\ [/tex]

Hence, Required answer is option (c) 5.

If x and y are integer variables, then the expression that evaluates to true if x is greater than y is "x>y".

In Java, symbol of ">" is used for "greater-than" operator. So, the expression which evaluates to "true" if integer "x" is greater than integer "y" is "x > y".

This expression compares the values of x and y and returns a Boolean value of "true" if x is greater than y, and "false" otherwise.

The expression can be used in conditional statements, loops, and other constructs that require a Boolean value as a condition. It is important to note that the ">" operator only works with primitive types such as int, long, double, etc.

Learn more about Expression here

https://brainly.com/question/30706198

#SPJ4

Answer:

[tex](x-4)^2+(y+1)^2=162[/tex]

Step-by-step explanation:

Determine r² by using the equation of a circle and plugging in the center (h,k)->(4,-1) as well as (x,y)->(13,8):

[tex](x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-(-1))^2=r^2\\(13-4)^2+(8+1)^2=r^2\\9^2+9^2=r^2\\81+81=r^2\\162=r^2\\[/tex]

Hence, the equation of the circle that meets these criteria is[tex](x-4)^2+(y+1)^2=162[/tex]

Answer:

7 miles

Step-by-step explanation:

Note there are 63,360 inches in a mile.

So, rewrite scale as 1 inch: 1 mile, where inch replaces the unit.

Therefore 7 inches: 7 miles.

The factorization of the polynomial x³ + 9x² + 3x + 27 by grouping is:

x³ + 9x² + 3x + 27 = (x + 9)(x² + 3)

In algebra, "grouping" refers to a method of factoring polynomials that involves grouping together pairs of terms within the polynomial, in order to factor out a common factor.

In mathematics, a polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

In the given question,

To factor the four-term polynomial by grouping, we can follow these steps:

Step 1: Group the first two terms and the last two terms together.

x³ + 9x² + 3x + 27

= (x³ + 9x²) + (3x + 27)

Step 2: Factor out the common factor from each group.

= x²(x + 9) + 3(x + 9)

Step 3: Notice that the expression (x + 9) is a common factor of both terms, and factor it out.

= (x + 9)(x² + 3)

Therefore, the factorization of the polynomial x³ + 9x² + 3x + 27 by grouping is:

x³ + 9x² + 3x + 27 = (x + 9)(x² + 3).

To know more about factorization , visit:

https://brainly.com/question/14549998

#SPJ1

0-24-  Tally (1)

25-49   Tally (4)

50-74  Tally (5)

75-99  Tally (2)

There are 3 seniors who take Math and Spanish, but not Physics.

What is Venn Diagram?

A diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by the areas of overlap among the circles.

To solve this problem, we can use a Venn diagram to organize the information given about the students.

First, we know that there are 150 seniors in total, so we can label the outer rectangle of the Venn diagram as having a total of 150 students.

Next, we can label the three circles as Math, Spanish, and Physics, with the numbers given in the problem:

80 seniors take Math, so we label the Math circle with 80.

41 seniors take Spanish, so we label the Spanish circle with 41.

54 seniors take Physics, so we label the Physics circle with 54.

We also know that 10 seniors take Math and Spanish, 19 take Math and Physics, 12 take Physics and Spanish, and 7 take all three. We can label these overlaps in the Venn diagram as follows:

The overlap of Math and Spanish is 10.

The overlap of Math and Physics is 19.

The overlap of Physics and Spanish is 12.

The overlap of all three is 7.

To find the number of seniors who take Math and Spanish, but not Physics, we need to subtract the number of seniors who take all three (because they are counted in all three circles) and the number of seniors who take Math, Spanish, and Physics (because they are counted in the overlap of all three circles). Then we add the number of seniors who take only Math and Spanish (because they are not counted in the Physics circle).

Using the formula for the number of elements in the union of three sets, we have:

Math or Spanish or Physics = Math + Spanish + Physics - (Math and Spanish) - (Math and Physics) - (Spanish and Physics) + (Math and Spanish and Physics)

So, the number of seniors who take Math and Spanish, but not Physics is:

Math and Spanish - (Math and Spanish and Physics) + (Math or Spanish or Physics - (Math + Spanish + Physics) + (Math and Spanish and Physics))

= 10 - 7 + (80 + 41 + 54 - 2(10) - 2(19) - 2(12) + 7)

= 3

Therefore, there are 3 seniors who take Math and Spanish, but not Physics.

To learn more about Venn Diagram, click on the link:

https://brainly.com/question/2099071

#SPJ1

Jadi, lebar jalan adalah 14 meter.

Untuk Konsultasi Tugas Lainnya: 0813-7200-6413

Answer:

Matt would walk 8 miles in to hours.

Step-by-step explanation:

15 minutes is 1/4 of an hour, meaning it would be 1/8 of 2 hours.

1 mile times 8 = 8 miles

Hope that helps!

The area of the composite figure is 159.9 cm²

From the question, we are to determine the area of the given composite figure

In the given diagram, the area of the composite figure = Area of triangle + Area of rectangle

First, we will calculate the area of the triangle

Area of triangle = 1/2 × base × height

Thus,

Area of the triangle = 1/2 × 16.4 × 5.5

Area of the triangle = 45.1 cm²

Calculating the area of the rectangle

Area of rectangle = Length × Width

Thus,  

Area of the rectangle = 16.4 × 7

Area of the rectangle = 114.8 cm²

Therefore,

The area of the composite figure = 45.1 cm² + 114.8 cm²

The area of the composite figure = 159.9 cm²

Hence, the area is 159.9 cm²

Learn more on Calculating the area of the composite figure here: https://brainly.com/question/10254615

#SPJ1

Answer:

95.07[tex]m^{2}[/tex]

Step-by-step explanation:

You need to work out the area of a cicle, since the goat can only move 5.5m round

Area of a cicle = π r²

π = 22/7

r=5.5m

[tex]\frac{22}{7}[/tex] x [tex]5.5^{2}[/tex] = 95.07142857 = 95.07[tex]m^{2}[/tex] (to 2d.p)

Answer:

94.79 square meters.

Step-by-step explanation:

Assuming the goat is tied to the peg in the ground, the area that the goat can graze on can be represented by a circle with radius equal to the length of the rope.

Given that the length of the rope is 5.5 meters, the radius of the circle can be calculated as:

r = length of rope = 5.5 meters

The area of a circle is given by the formula:

A = πr²

where π (pi) is approximately equal to 22/7 or 3.14.

So, substituting the value of r, we get:

A = π × (5.5)²

= 3.14 × (5.5)²

= 3.14 × 30.25

= 94.79 square meters (approx.)

Therefore, the area of grass that the goat can eat is approximately 94.79 square meters.

Answer: the distribution to the x and the 3 makes the solution 4

Step-by-step explanation: i got you broski

By using sample standard deviation - (1) N or n = 20

(2) X or μ = 43.4

(3) σ = 9.78 and s = 10.04

Why does sample standard deviation exist?

When we talk about a sample standard deviation, we're not talking about population standard deviation. The average amount by which a group of values deviates from their mean is shown by the statistical measure of variability known as the standard deviation.

We are given with the following data set below;

{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}

(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.

(2) The formula for calculating Mean of the data, i.e. X or μ is given by;

       Mean  =  51 +48+ 42+ 43+ 48 + 48 + 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42/20

                = 868/20 = 43.4

So, the value of  X or μ   is 43.4.

(3) The formula for calculating population standard deviation () is given by;

  Standard deviation, σ  = √(51 - 43.4)² + (48 - 43.4)² + .........+(42 - 43.4)²/20

        =  9.78

Similarly, the formula for calculating sample standard deviation (s) is given by;

       Sample Standard deviation, s =  

                       √(51 - 43.4)² + (48 - 43.4)² + .........+(42 - 43.4)²/20 - 1

                      =  10.04

Learn more about sample standard deviation

brainly.com/question/24277447

#SPJ1

Michelle would earn about $807.69 per week if she took the clerk job, rather than the administration job.

Earnings refer to the amount of money that an individual or entity has earned or generated through its business activities or work. In the context of an individual, earnings usually refer to the amount of money that a person receives as compensation for their work, such as salaries, wages, commissions, tips, bonuses, or any other form of payment for services rendered.

Earnings can also refer to the amount of money that a company generates from its business activities, such as sales revenue, profits, or earnings per share. This information is often used by investors, analysts, and other stakeholders to evaluate the financial performance of a company and make investment decisions.

To calculate Michelle's weekly earnings if she took the clerk job, we need to first calculate her biweekly earnings:

42,000 / 26 = 1,615.38 (her biweekly earnings as a clerk)

To find her weekly earnings, we can divide this number by 2:

1,615.38 / 2 = 807.69 (her weekly earnings as a clerk)

To find out how much she would earn per week if she took the administration job, we can simply divide the annual salary by the number of weeks in a year:

853 / 52 = 16.40 (her weekly earnings as an administrator)

Therefore, Michelle would earn about $807.69 per week if she took the clerk job, rather than the administration job.

To know more about salary  visit:

https://brainly.com/question/28811805

#SPJ1

If we solve this inequality for x, we get x 20, which indicates the school equation bake sale must sell at least 20 cakes in order to meet their $200 objective.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

10x ≥ 200 accurately portrays the scenario.

To explain why, consider the following:

Because each cake costs $10, the total amount earned from selling x cakes is 10x.

The aim is to raise at least $200, thus the total amount must be larger than or equal to $200.

As a result, we may describe the circumstance by writing the inequality 10x 200.

If we solve this inequality for x, we get x 20, which indicates the school bake sale must sell at least 20 cakes in order to meet their $200 objective.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

Step-by-step explanation:

central rectangle area

(A=LxW)

7x4=28 units^2,

congruent triangle area

(1/2bxh)

1/2( 7x2)= 7 units^2. (one triangle)

let's add the 3 areas 28 + 7 + 7 = 42 units^2 (your answer)

The population will be 482,720 in 405 years using exponential model that doubles its size every 81 years.

A form of growth known as exponential growth occurs when a quantity's rate of expansion is proportionate to its present value. In other words, the amount increases with time at a faster pace. Several natural and artificial processes, including population expansion, compound interest, and the spread of contagious illnesses, exhibit exponential growth.

The population increases using the exponential model given as:

[tex]P(t) = P_0 * 2^{(t/x)}[/tex]

Substituting the values P₀ = 15,085 and x = 81.

[tex]P(405) = 15,085 * 2^{(405/81)}\\P(405) = 15,085 * 2^5\\P(405) = 15,085 * 32\\P(405) = 482,720[/tex]

Hence, the population will be 482,720 in 405 years using exponential model, that doubles its size every 81 years.

Learn more about exponential growth here:

https://brainly.com/question/11487261

#SPJ1

Answer: x=16, y=9

Step-by-step explanation:  Find x first. The unmarked angle underneath the x + 19 is 9x + 1 (corresponding angles so congruent so same measure as the angle below)

So the two angles add up to 180°

x+19 + 9x + 1 = 180°

combine like terms

10x + 20 = 180

subtract 20

10x = 160

divide by 10

x = 16

Now you can find the measure of the angle marked 9x+1.

9(16) + 1

= 144 + 1

= 145

Now find y. The angle marked 9x+1 is now known to be a 145° angle. So that angle with the angle marked 3y+8 must make 180°

3y + 8 + 145 = 180

combine like terms

3y + 153 = 180

subtract 153

3y = 27

divide by 3

y = 9

-Hope this helps! Thanks, have a good day :-)

Answer:

Step-by-step explanation:

long leg = 78  (means that 26√3*√3 = 26√9 = 26*3 = 78

for x: Short leg= 26√3

Hypotenuse= 2*26√3 = 52√3 for y

a) The value of Hy = 1.15

b) The proportion of cartons with less than 1.15 broken eggs is 0.60

c) The answer is B)This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like.

(a) Hy = 0.67, which means that on average, there are 0.67 broken eggs per carton.

Hy = (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1

= 0.67

(b) The proportion of cartons with less than 0.67 broken eggs is 0.60 which is probability of 0 broken eggs.. This may be surprising as the probability of having less than 0.67 broken eggs is only 0.60, but this is due to the fact that the distribution is skewed towards higher values.

(c) Hy is not equal to the simple average of 0, 1, 2, 3, and 4 because the distribution is not symmetrical. The probabilities are weighted towards higher values, which increases the mean. Additionally, the value of zero should be included in the calculation, as it represents a possible outcome. Therefore, the correct formula for Hy is (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1 = 0.67.

To know more on symmetrical distribution

https://brainly.com/question/31184447

#SPJ4

--The question is incomplete, answering to the question below--

"Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs.

y 0 1 2 3 4

p(y) 0.60 0.20 0.15 0.03 0.02

(a) Calculate and interpret Hy  

(b) In the long run, for what proportion of cartons is the number of broken eggs less than Hy? (Round your answer to two decimal places).

Does this surprise you?

Yes

No

(c) Explain why Hy is not equal to (0 + 1 + 2 + 3 + 4)/5 = 2.0.  

A. This computation of the mean is incorrect because the value in the denominator should equal the maximum y value.

B. This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like

C. This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when

D. This computation of the mean is incorrect because it does not take into account the number of partially broken eggs."

In both cases, the sum of x and y is not divisible by 3, we have demonstrated that the proposition is true. and the proposition is false, and we have shown a counterexample where the sum of two integers, one of which is not divisible by 3 and the other is divisible by 3, can be divisible by 3.

(a) To prove that the sum of two integers, x and y, neither of which is divisible by 3, cannot be divisible by 3, we can use a case-based proof.

Case 1: x and y leave a remainder of 1 when divided by 3.

Let x = 3m + 1 and y = 3n + 1, where m and n are integers. Then, the sum of x and y is 3m + 3n + 2, which leaves a remainder of 2 when divided by 3. Therefore, x + y is not divisible by 3.

Case 2: x and y leave a remainder of 2 when divided by 3.

Let x = 3m + 2 and y = 3n + 2, where m and n are integers. Then, the sum of x and y is 3m + 3n + 4, which leaves a remainder of 1 when divided by 3. Therefore, x + y is not divisible by 3.

Since in both cases, the sum of x and y is not divisible by 3, we have  demonstrated that the proposition is true.

(b) To prove that the sum of two integers, x and y, where x is not divisible by 3 and y is divisible by 3, cannot be divisible by 3, we can use a counterexample.

Let x = 2 and y = 6. Then, x is not divisible by 3 and y is divisible by 3. However, x + y = 8, which is not divisible by 3.

Therefore, the proposition is false, and we have shown a counterexample where the sum of two integers, one of which is not divisible by 3 and the other is divisible by 3, can be divisible by 3.

To know more about proposition click here:

brainly.com/question/30895311

#SPJ4

Answer:

7. 23      

8. (3 - 8) x 5

Step-by-step explanation:

I think the second one is right but I know the first one is.

The line segment AB and CB are perpendicular to each other.

Check whether the slopes of the lines are the negative reciprocals of one another to see if they are perpendicular to one another. The steps are as follows:

Learn more about Coordinates here:

brainly.com/question/18269861

#SPJ1

The probability of waiting at least 26 minutes is 0.316. The average waiting time is 19 minutes.

Step 1:

The probability of waiting at least 26 minutes can be calculated by finding the area under the probability density function from 26 to 38:

P(waiting at least 26 minutes) = ∫26^38 (1/38) dt = [t/38] from 26 to 38

= (38/38) - (26/38) = 12/38 = 0.316

So the probability of waiting at least 26 minutes is 0.316 or approximately 0.316 rounded to 3 decimal places.

Step 2:

The average waiting time can be calculated by finding the expected value of the probability density function:

E(waiting time) = ∫0³⁸ t f(t) dt = ∫0³⁸ (t/38) dt

= [(t²)/(238)] from 0 to 38

= (38²)/(238) = 19

Therefore, the average waiting time is 19 minutes.

Learn more about probability here: brainly.com/question/30034780
#SPJ4

Answer: y=3x+0

Step-by-step explanation: rise (y) over run (x) would be 3/1, which is 3. The line passes through the origin (0,0) so its 0.

Answer:

B

Step-by-step explanation:

It's like a piece of paper, fold it in half

Answer:

I HOPE ITS HELPFUL

Step-by-step explanation:

Cost price of 300 articles = ₹1500Hence cost of each item = 1500/300 = ₹5With 20% profit, selling price of each item = 5 * 120/100 = ₹6Hence, total selling price of 260 items = 260 * 6 = ₹1560Selling price of balance items = 6/2 = ₹3Total selling price for balance items = 40 * 3 = ₹120Total selling price = 1560 + 120 = ₹1680Profit gained = 1680 - 1500 = ₹180Profit percentage = 180/1500 * 100 = 12