Factoring polynomials
-12n2-11n=-15

Answer:

500 centimeters

Step-by-step explanation:

Answer:

500 Centimeters

Step-by-step explanation:

(a) We have shown that there exists an element b ∈ B that is an upper bound for A.

(b) The statement in part (a) is not always the case if we only assume sup A ≤ sup B.

(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.

Proof:
1. By definition, sup A is the least upper bound for set A, and sup B is the least upper bound for set B.
2. Since sup A < sup B, there must be a value between sup A and sup B.
3. Let's call this value x, where sup A < x < sup B.
4. Now, since x < sup B and sup B is the least upper bound of set B, there must be an element b ∈ B such that b > x (otherwise, x would be the least upper bound for B, which contradicts the definition of sup B).
5. Since x > sup A and b > x, it follows that b > sup A.
6. As sup A is an upper bound for A, it implies that b is also an upper bound for A (b > sup A ≥ every element in A).

Thus, we have shown that there exists an element b ∈ B that is an upper bound for A.

(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.

Example:
Let A = {1, 2, 3} and B = {3, 4, 5}.
Here, sup A = 3 and sup B = 5. We can see that sup A ≤ sup B, but there is no element b ∈ B that is an upper bound for A, as the smallest element in B (3) is equal to the largest element in A, but not greater than it.

This example shows that the statement in part (a) is not always the case if we only assume sup A ≤ sup B.

Visit here to learn more about upper bound:

brainly.com/question/22965427

#SPJ11

The random variable expressed as the conditional expectation of Y given X is E[Y|X]=1/2(X−Y).

Two independent Bernoulli r.v., U and V, both with probability of success 1/2. Let X=U+V and Y=∣U−V∣.To calculateThe covariance of X and Y (σX,Y) and if X and Y are independent and the random variable expressed as the conditional expectation of Y given X, i.e., E[Y∣X].Solution(a) Calculation of covariance of X and Y, σX,YUsing the properties of covariance, we have:  σX,Y=E[XY]−E[X]E[Y]​.

Using the expectation calculated above, we can now find the covariance of X and Y as follows:σX,Y=E[XY] Thus, the covariance of X and Y is σX,Y=3/4.(b) Checking independence of X and Y In order to show that X and Y are independent, we need to show that their covariance is zero, i.e., σX,Y=0.

To know more about variable visit:

https://brainly.com/question/16906863

#SPJ11

Answer:

------------------

Let the amount deposited be x. It is assumed we are talking about simple interest.

After 4 years the interest amount is:

95% of this amount is Rs 4940:

Mrs Majhi deposited Rs 20000.

Mrs. Majhi deposited Rs 20000 in her bank account. This was calculated by first finding the total interest (before tax) and then using the formula for simple interest to determine the principal amount.

The question is based on the concepts of Simple Interest and taxation. We know that Mrs Majhi received Rs 4940 as net interest after 4 years and this amount is 95% of the total interest (since 5% was paid as income tax). The total interest can be calculated as (4940 / 95) * 100 = Rs 5200.

The rate of interest is given as 6.5% per annum. Thus, the money deposited (Principal) by her can be calculated using the formula for simple interest (I = PRT/100), where P is the Principal, R is the rate of interest, and T is the time. Re-arranged to calculate the Principal (P), it becomes P = I / (R*T) = 5200 / (6.5*4) = Rs 20000.

https://brainly.com/question/32543341

#SPJ2

Answer:

y = -5

o = 35 degrees

Step-by-step explanation:

If you replace y with -5, the statement  7y = 4y - 15 is correct. You get -35 =  -35. Hope this helped!

The probability of winning being consistently 10 percent less than expected indicates an unfair game or a biased system.

In a fair game or system, the probability of winning should be represented by the ratio of favorable outcomes to total outcomes. This is commonly expressed as a fraction a/b, where a represents the number of favorable outcomes and b represents the total number of possible outcomes.

However, if the probability of winning is always 10 percent less than expected, it suggests that there is a systematic bias or manipulation in the game or system. This bias could be intentional, designed to favor certain individuals or entities, or it could be due to some inherent flaw or error in the system.

The consistent 10 percent reduction in the probability of winning indicates that the game or system is not operating in a fair and unbiased manner. It raises concerns about fairness, integrity, and potentially unethical practices.

In summary, when the probability of winning is consistently 10 percent less than expected, it suggests the presence of an unfair game or biased system, where the outcomes are intentionally manipulated or influenced to give an advantage to certain parties.

To learn more about probability, click here: brainly.com/question/12594357

#SPJ11

Steps (A) 2(x² + 6x + 9) = 3 + 18 and (B) 2(x² + 6x) = 3 can be used to solve the given quadratic equation.

An algebraic equation of the second degree in x is a quadratic equation.

The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

So, let's examine the first option:

2(x² + 6x + 9) = 3 + 18

We'll now multiply 2 by each component of the other multiplier on the left:

2·x² + 2·6x + 2·9 = 3 + 18

2x² + 12x + 18 = 3 + 18

2x² + 12x - 3 = 18 - 18

2x² + 12x - 3 = 0

Let's examine the second option:

2(x² + 6x) = 3

We'll now multiply 2 by each component of the other multiplier on the left:

2·x² + 2·6x = 3

2x² + 12x = 3

2x² + 12x - 3 = 0

Therefore, steps (A) 2(x² + 6x + 9) = 3 + 18 and (B) 2(x² + 6x) = 3 can be used to solve the given quadratic equation.

Know more about quadratic equations here:

https://brainly.com/question/1214333

#SPJ1

Correct question:

Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Check all that apply.

A. 2(x2 + 6x + 9) = 3 + 18

B. 2(x2 + 6x) = –3

C. 2(x2 + 6x) = 3

x + 3 =

D. 2(x2 + 6x + 9) = –3 + 9

(x + 3)2 =

225 ml of water should be added to 25 ml of concentrated solution to get a diluted solution with a concentration of 10%.

Define the term diluted solution.

A diluted solution is a solution that has been made weaker or less concentrated by adding more solvent (usually water) to a concentrated solution. It contains a smaller amount of solute per unit volume of solution than the original concentrated solution.

Assuming the concentration of the concentrated solution is 100%, and we want to dilute it to a concentration of 10%, we can use the formula:

C1V1 = C2V2

Where:

C1 is the concentration of the concentrated solution (100% or 1.0)

V1 is the volume of the concentrated solution (25 ml)

C2 is the concentration of the diluted solution (10% or 0.1)

V2 is the volume of the diluted solution (unknown)

Rearranging the formula to solve for V2, we get:

V2 = (C1V1) / C2

Now Plug in the values we have, we get:

V2 = (1.0 x 25 ml) / 0.1

V2 = 250OW  ml

Therefore, we need to add 225 ml of water to 25 ml of concentrated solution to get a diluted solution with a concentration of 10%.

To learn more about diluted solutions click here

https://brainly.com/question/1615979

#SPJ1

On a Saturday afternoon, a family of five went to see a matinée movie. Everyone paid the same price for their movie tickets. The equation will be 57.50 = 5x + 25 and the value of x is $6.50.

Let the price of one movie ticket be x,

So if there are 5 members and the ticket price is same for all, the total price for 5 movie tickets = Price of one ticket × 5

= x × 5

= 5x

Money spent on drinks = $25

ow, the total money spent is $57.50

Total money spent = money spent on movie tickets + money spent on drinks

So, the equation will be:

57.50 = 5x + 25

Now, on solving the equation:

5x = 57.50 - 25

5x = 32.50

x = 32.50 / 5

x = 6.50

Hence, the price of one ticket is $6.50 and the equation for this question is 57.50 = 5x + 25.

To know more about equation:

https://brainly.com/question/3901911

#SPJ1

The effect on the graph of the function f(x) = x^2 when it is transformed to create the graph of h(x) = (1/5) f(x) is that the graph is compressed vertically by a factor of 1/5.

To see why this is the case, note that the factor of 1/5 in the equation for h(x) means that every y-value of the original function f(x) is divided by 5. This means that the vertical distance between any two points on the graph of h(x) will be 1/5th of the corresponding distance between those points on the graph of f(x). For example, if f(x) has a point (2,4) on its graph (i.e. f(2) = 4), then h(x) will have a corresponding point (2,4/5) on its graph (i.e. h(2) = (1/5)f(2) = (1/5)4 = 4/5). So the point (2,4) on the graph of f(x) is transformed to the point (2,4/5) on the graph of h(x). Since the y-coordinate of this point is divided by 5, the graph of h(x) is compressed vertically by a factor of 1/5 relative to the graph of f(x).

To learn more about transformation here:

https://brainly.com/question/29018533

#SPJ1

The variables of the test statistic may be determined to be \($s _1$\), \($s _2$\), \($n_ 1, n _2$\), t, which is the t - distribution test statistic, and \($x _1, x _2$\), which is the mean of the two samples.

When the variances of the two groups are not equal, pooled standard deviation estimations cannot be used. As an alternative, we must determine the standard error for each group separately. The variables of the test statistic may be determined to be \($s _1$\), \($s _2$\), \($n_ 1, n _2$\), t, which is the t - distribution test statistic, and \($x _1, x _2$\), which is the mean of the two samples.

The formula for this type of test statistic is given by -

\($t=\frac{x_1-x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{x_2}{n_2}}}$$\)

Here, the variables can be defined as below -

\($s_1^2, s_2^2=$\) variance of two samples

\($n_1, n_2=$\) respective sizes of the two samples

t = t - distribution test statistic

\($x_1, x_2=$\) Mean of the two samples

As a result, the variables of the test statistic can be determined to be \($s _1, s _2$\), which represents the variance of two samples, \($n _1, n _2$\), which represents the size of the two samples, t, which represents the t-distribution test statistic, and \($x _1, x _2$\), which represents the mean of the two samples.

The complete question is:

The formula for the test statistic used for a two sample test of means where the population variances are unknown and unequal is:

t = X1−X2√s12/n1+s22/n2X1-X2s12/n1+s22/n2

Match the variables to their description.

To learn more about test statistic refer to:

brainly.com/question/14128303

#SPJ4

Answer:

a). -8    b). 4/19

Step-by-step explanation:

F(x)= x²+9x       g(x)=1/x.

g(-1) = 1/ - 1

= -1

f(-1) = x²+9x

= -1² + 9(-1)

= 1 - 9

= -8

G(f(1/2))

f(1/2) = x²+9x

= 1/2² + 9(1/2)

= 1/4 + 9/2

= 19/4

g (19/4) = 1/x

= 1/19/4

= 4/19

Answer:

1). -8    2). 4/19

Step-by-step explanation:

F(x)= x²+9x       g(x)=1/x.

g(-1) = 1/ - 1

= -1

f(-1) = x²+9x

= -1² + 9(-1)

= 1 - 9

= -8

G(f(1/2))

f(1/2) = x²+9x

= 1/2² + 9(1/2)

= 1/4 + 9/2

= 19/4

g (19/4) = 1/x

= 1/19/4

= 4/19

Answer:

p=  y=6x+2

Q=  y=-2x+2.5

Step-by-step explanation:

the formula is y=mx+b

M=slope

B=y-intercept

The y-intercept is the number that your line goes through

The slope is two ordered pairs where you use the formula rise over run to find your slope.

Answer:

Should be 3.9

Step-by-step explanation:

prove me wrong

The linear equation represented by the table (-2,7) (1,4) (3,2) (6,-1) is y = -x + 5. To find the linear equation represented by the table (-2,7) (1,4) (3,2) (6,-1), we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope, which is the change in y over the change in x between any two points. Let's choose the points (1,4) and (3,2):

slope = (y2 - y1) / (x2 - x1)
     = (2 - 4) / (3 - 1)
     = -2 / 2
     = -1

Now that we have the slope, we can plug it in to the slope-intercept form and solve for b using one of the points. Let's use the point (1,4):

4 = (-1)(1) + b
b = 5

So the equation of the line is y = -x + 5.

To check our work, we can plug in the other points and make sure they all satisfy the equation:

-2 = (-1)(-2) + 5 (true)
7 = (-1)(-2) + 5 (true)
2 = (-1)(3) + 5 (true)
-1 = (-1)(6) + 5 (true)

Therefore, the linear equation represented by the table (-2,7) (1,4) (3,2) (6,-1) is y = -x + 5.

Learn more about linear equation here:

brainly.com/question/28307569

#SPJ11

Answer:

Step-by-step explanation:

Given angle 1 = 140°, you want the measures of the other numbered angles where a transversal crosses parallel lines.

Where a transversal crosses parallel lines, corresponding angles are congruent.

Wherever lines cross. vertical angles are congruent, and linear pairs are supplementary.

These reasons together tell you all the obtuse angles are congruent, and all the acute angles are congruent. The obtuse and acute angles are supplementary.

  ∠1 = ∠4 = ∠5 = ∠8 = 140° . . . . . . given

  ∠2 = ∠3 = ∠6 = ∠7 = 40° . . . . . . done for you

__

Additional comment

The angles are also named according to where pairs of angles are found.

Various theorems describe the congruent/supplementary status of pairs of angles using these names:

In general, the converses of these theorems are also true. If corresponding angles are congruent, then the lines are parallel.

Answer: True

Here's an example:

6 x 8 = 48

48/ 4 = 12

14 x 12 = 168

168/4 = 42

The counterclockwise circulation around c is 12 and the outward flux through c is zero.

Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.

In this case,

we have a field f=(7x−4y)i+(9y−4x)j and

a square curve c bounded by x=0, x=4, y=0, y=4.

To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.

The curl of f is given by (0,0,3), so the line integral evaluates to 12.

To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.

To learn more about : circulation

https://brainly.com/question/30619471

#SPJ11

Answer: 1513.50=961.50+46x

The number of players the team can bring to the tournament = 12.

Step-by-step explanation:

Let x= the number of players the team can bring to the tournament.

Total money raised = Rent of bus + (Cost per player) (Number of players)

\(1513.50=961.50+46x\\\\\Rightarrow\ 46x=1513.50-961.50\\\\\Rightarrow\ 46x = 552\\\\\Rightarrow x=\dfrac{552}{46}\\\\\Rightarrow x=12\)

Hence, the number of players the team can bring to the tournament = 12.

Answer:

All numbers divisible by 9 are also divisible by 3.

Step-by-step explanation:

Nine is basically just 3 3's.

A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

To know more about Demand Matrix here

https://brainly.com/question/13012912

#SPJ4

The number of men living in the village is 260.

A collection of many linear equations that include the same variables is referred to as a system of linear equations. A linear equation system is often composed of two or more linear equations with two or more variables.A linear equation with two variables, x and y, has the following general form:

                                           \(ax + by = c\)

Given:

Total inhabitants in the village: 817

Number of children: 241

There are 56 more women than men in the village

Total adults = Total inhabitants - Number of children

Total adults = 817 - 241

Total adults = 576

Let number of men in the village be 'x' and number of women in the village be 'y',

∴ y=x+56 (given) ..................(1)

Also, x+y=576 .................(2)

From equation (1) and (2),

x + (x + 56) = 576

2x + 56 = 576

2x = 576 - 56

2x = 520

x = 520 / 2

x = 260

Learn more about linear equations here:

brainly.com/question/29739212

#SPJ1

Answer:

I believe its A. 7/16 inches per hour

Step-by-step explanation:

This is wrong don't put this

Answer:

The volume of the spherical grain is of 1.13*10^-7 cubic centimeters.

Step-by-step explanation:

The volume of a sphere with radius r is given by the following formula:

In this question:

The spherical grain has volume of 5*10^-3 centimeters = 0.005. So r = 0.005. Then

The volume of the spherical grain is of 1.13*10^-7 cubic centimeters.

The probability that we did not see all three colors is \($\frac{13}{16}\)

Consider the event,

A: Did not see all 3 colors

Complement of the event A is A’ where

A' : All colors were seen

Since 3 balls are drawn and all colors should be seen, it implies that there is 1 ball of each color

It is required to find P(A) = P(did not see all colors)

By the probability rule for complement:

P(A)  =1-P(A')

P(A') & =P(all colors were seen )

=P(1 White AND 1 Green AND 1 Red )

Total number of balls = 4

Number of combinations of 3 balls possible = 64

Since drawing a ball is with replacement, we have the following number of combinations with each color represented where R1 and R2 are the two red balls.

The table attached at end of the solution

Total number of combinations with each color represented = 12

Thus the probability of A’ is:

\($P\left(A^{\prime}\right) & =\frac{12}{64} \\\)

\($P(A) & =1-\frac{12}{64} \\\)

\($=\frac{52}{64} \\\)

\($=\frac{13}{16}\)

Hence, the required probability P(did not see all 3 colors) is \($\frac{13}{16}$\)

For more questions on probability

https://brainly.com/question/13042371

#SPJ4

Answer:

6.18 ft

Step-by-step explanation:

The ramp forms a right triangle.

We know two of the lengths of the right triangle, therefore, we would apply pythagorean theorem to find the longest length of the triangle, which is the length of the ramp.

The given lengths are 1.5 ft and 6 ft. The length of the ramp is the length of the longest side (hypotenuse length).

Thus, applying pythagorean theorem:

\( c^2 = a^2 + b^2 \), where,

a = 1.5 ft

b = 6 ft

c = length of ramp

Substituting the values:

\( c^2 = 1.5^2 + 6^2 \)

\( c^2 = 2.25 + 36 \)

\( c^2 = 38.25 \)

\( \sqrt{c^2} = \sqrt{38.25} \)

\( c = \sqrt{38.25} \)

\( c = 6.18 \) (nearest hundredth)

length of the ramp = 6.18 ft