Factor each polynomial using the difference of two squares patt
square trinomial pattern.
x² – 9

Answer:

0.25 pounds

Step-by-step explanation:

((3/5) pound) - (0.35 pounds) = 0.25 pounds

Answer: graph b

Step-by-step explanation:

Vertex:  ( 3 ,0 )

Focus:  ( 3 , 1 4 )

Axis of Symmetry:  x = 3

Directrix:  y = − 1 4

To answer this question, we need to know the median and upper quartile of the data set. Once we have these values, we can determine what percentage of the data falls to the right of the median and to the left of the upper quartile.
Let's say the median of the data set is 50 and the upper quartile is 75. To find the percentage of measurements to the right of the median, we need to look at the data values that are greater than 50 and divide that number by the total number of measurements. Let's say there are 40 data values greater than 50 and a total of 100 measurements.

Then, the percentage of measurements to the right of the median would be:

(40/100) x 100% = 40%

To find the percentage of measurements to the left of the upper quartile, we need to look at the data values that are less than or equal to 75 and divide that number by the total number of measurements. Let's say there are 60 data values less than or equal to 75 and a total of 100 measurements. Then, the percentage of measurements to the left of the upper quartile would be:

(60/100) x 100% = 60%


Your answer:
1. 40% of the measurements lie to the right of the median.
2. 60% of the measurements lie to the left of the upper quartile (Q3).

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1. (a) To be sure of getting at least 3 cards from one suit, we can consider the worst-case scenario where we select cards from each of the four suits equally until we have 2 cards from each suit.

In this case, we will have a total of 2 x 4 = 8 cards.


However, selecting the 9th card will guarantee that we have at least 3 cards from one suit. Therefore, we need to select a minimum of 9 cards to be sure of getting at least 3 cards from one suit.

(b) To be sure of getting at least 3 diamonds, we can again consider the worst-case scenario where we select cards from the other suits until we have 2 diamonds. In this case, we will have a total of 2 + 3 x 13 = 41 cards.

However, selecting the 42nd card will guarantee that we have at least 3 diamonds. Therefore, we need to select a minimum of 42 cards to be sure of getting at least 3 diamonds.

2. To be sure of getting an integer that is divisible by both 5 and 117, we need to consider the least common multiple (LCM) of 5 and 117, which is 585. Therefore, we need to pick a minimum of 585 integers from 1 through 500 to be certain of getting one that is divisible by both 5 and 117.

3. (a) To choose a committee of six that contains three men and three women, we need to select 3 men from the 5 available men and 3 women from the 7 available women. The number of ways to choose 3 men from 5 is denoted by “5 choose 3” or C(5, 3), which is calculated as C(5, 3) = 5! / (3! * (5 – 3)!) = 10. Similarly, the number of ways to choose 3 women from 7 is C(7, 3) = 7! / (3! * (7 – 3)!) = 35. The total number of committees with three men and three women is the product of these two combinations: 10 * 35 = 350.


(b) To calculate the number of committees of six that contain at least two men, we can consider two cases: exactly two men and three men.

For exactly two men, we choose 2 men from the 5 available men and 4 members (women) from the remaining 7 members. The number of ways is C(5, 2) * C(7, 4) = 10 * 35 = 350.

For three men, we choose 3 men from the 5 available men and 3 members (women) from the remaining 7 members. The number of ways is C(5, 3) * C(7, 3) = 10 * 35 = 350.

Therefore, the total number of committees with at least two men is 350 + 350 = 700.


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The domain of f is the set of all real numbers f(x,y) as (x,y) varies throughout the domain D with three variables.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The functions of a point (or vector) in R2 or R3 that have real values will now be looked at. These functions will typically be defined on sets of points in R2, but there will be occasions when we utilise points in R3 and when it is more convenient to think of the points as vectors (or terminal points of vectors).

Each point f(x,y) in D is given a real number f(x,y) according to a real-valued function f defined on a subset D of R2. The domain of f is the set of all real numbers f(x,y) as (x,y) varies throughout the domain D, and the range of f is the greatest set D in R2 on which f is defined.

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Answer:

1) $30,000 + $12x

(2) $50x

(3) $38x - $30,000

(4) 790 CD's to break even

Given that,

Variable cost = $12 per CD

Fixed cost = $30,000

Selling price = $50 each

Let x be the number of CD's produced,

(1) Total cost function:

C(x) = Fixed cost + Variable cost

     = $30,000 + $12x

(2) Total revenue:

R(x) = Units produced × selling price of each unit

     = $50x

(3) Total profit:

P(x) = R(x) - C(x)

     = $50x - ($30,000 + $12x)

     = $50x - $30,000 - $12x

     = $38x - $30,000

(4) Number of CD's which must be produced to break even:

Total profit = 0

$38x - $30,000 = 0

x = $30,000 ÷ $38

 = 789.47 or 790 CD's to break even.

Hope this helps! :)

Answer:

C = (3, -3), D = (-2, -3)

Step-by-step explanation:

The distance between two points \((x_1,y_1)\ and\ (x_2,y_2)\) on the coordinate plane is given by:

\(Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Points ABCD form a rectangle with an area of 30 unit². Points A and B are located at A(-2, 3) and B(3, 3). The distance between A and B is:

\(|AB|=\sqrt{(3-(-2))^2+(3-3)^2}=5\ units\)

|AB| = width = 5 units

Area of ABCD = |AB| * |BC|

30 = 5 * |BC|

|BC| = length = 6 units

Let point C be located at (c, d). Since point C is below point B, hence the c coordinate of point B would be the same as that of C. Hence C = (3, d)

\(|BC|=\sqrt{(3-3)^2+(d-3)^2} \\\\\sqrt{0+(d-3)^2}=6\\\\square\ both\ sides:\\\\(d-3) ^2=36\\\\take\ square\ root\ of\ both\ sides:\\\\d-3=\pm 6\\\\d=6+3\ or\ d=-6+3\\\\d=9\ or\ d=-3\\\\\)

Since point C is vertically below point B, hence the y coordinate would be negative

d = -3

C = (3, -3)

Point D would have the same y coordinate as point C since they are on the same horizontal line. Also, point D would have the same x coordinate as point A since it is vertically below point A. Hence:

D = (-2, -3)

Deshawn's marginal benefit if he sells a basic detailing package is: $15

A marginal advantage or benefit is a modest but demonstrable benefit that a buyer receives by purchasing an additional unit of an item or service.

As a customer decides to consume more of a single commodity, the marginal benefit typically decreases.

The following information about a car detailing service is given,

(a) The marginal advantage  or benefit is the extra benefit obtained by selling an additional unit. Because the detailing package costs $75, the profit from selling an extra item is $75. If DeShawn sells the standard bundle, the marginal benefit is $75.

(b) The marginal cost is the incremental cost of generating one more unit of output.

Because the worth of the detailing car's engine adds $20 to the bill.  As a result, the marginal cost of include engine detailing in the basic detailing package is $20.

(c) Compare the marginal benefit and marginal cost of offering engine detailing service to decide whether to give engine detailing service. The marginal cost of engine detailing service is twenty dollars.

DeShawn provides this service as part of the base package for S90, thus the marginal benefit is $15 [=$90 - $75].

DeShawn should not provide engine detailing services since the marginal benefit is less than the marginal expense of doing so.

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Answer:

C

Step-by-step explanation:

In order to solve this question, we need to use the z-score z of value x, belonging to a normal distribution with mean μ and standard deviation σ.

z is defined as:

In this problem, we have, in pounds:

μ = 8.9

σ = 1.1

PART 1

So, the percentage of domestic house cats that weigh less than 7.8 pounds is:

And from a z-score table, we have:

Therefore, the percentage of domestic house cats that weigh less than 7.8 pounds is approximately 0.1587 or 15.87%.

PART 2

The percentage of domestic house cats that weigh more than 11.1 pounds is 1 minus the percentage of them that weigh less than that:

Therefore, the percentage of domestic house cats that weigh more than 11.1 pounds is approximately 0.0228 or 2.28%.

PART 3

The domestic house cat weighing 9 pounds is in percentile P(x<9):

Therefore, a domestic house cat weighing 9 pounds is in the 54th percentile.

Answer:

\(\sqrt{231}\) cm

Step-by-step explanation:

The Pythagorean theorem is a mathematical principle that relates to the three sides of a right triangle. The formula for this is:

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

In this case, the hypotenuse (c) is 16 cm, and one of the legs (a) is 5 cm. We can plug in the values and solve for the missing value.

\(5^2+b^2=16^2\)

\(25+b^2=256\)

\(b^2=256-25\)

\(b^2=231\)

\(b = \sqrt{231}\) cm

Answer: a = 3, b = 2

Step-by-step explanation:

When a system of linear equations has no solution, they are parallel and do not share the same y-intercept.

Parallel lines have the same slope so a must equal 3.

The first equation's y-intercept is -2, so the only other option is b = 2.

Hope this helps!

Answer:

28

Step-by-step explanation:

f(-1)=-2(-1)^2

f(-1)=2*1

f(-1)=2

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

g(-4)=2+12

g(-4)=14

f(-1)*g(-4)=2*14=28

Explanation

to know the total bill amount we need to add the tip to the total,so

Step 1

find the value of the tip

it means to find the tip amount you need multiply the bill by 0.23,hence

Step 2

finally , add the values to know the total restaurant bill including the tip amount

So, the answer is $138.3627.

I hope this helps you

Answer:

Below.

Step-by-step explanation:

I can't see the words on your image very well but I can give you an explanation of the remainder theorem.

The theorem allows you to find the remainder of a division without doing the division itself.

You can find the remainder when  a polynomial is divided by a linear expression like 3x - 2, for example,  using this theorem.

An example will explain the method:

What is the remainder when x^3 - x^2 - 2x - 5 is divided by 2x - 1?

Put 2x - 1 = 0, this gives x = 0.5.

Now we plug x = 0.5 into the polynomial:

This = (0.5)^3 - (0.5)^2 -2(0.5) - 5 = -6.125

So the remainder is -6.125.

The formal definition is

The remainder when P(x) is divided by x - a is f(a).

Given: Frequency, n = 8 cycles/second. Distance between highest and lowest points, A = 8 cm.

To Find: Equation of the form y = A sin ωt that gives the distance of the mass from its rest position as a function of time.

Solution: Frequency, n = 8 cycles/second.

Therefore, Time period, T = 1/n = 1/8 s

Now, using the relationω = 2π /Tω = 2π * nω = 2π * 8ω = 16π rad/s

Distance between highest and lowest points, A = 8 cm. Now, the equation for the displacement of the particle from its mean position is given as: y = A sin (ωt)Putting the values of A and ω we get; y = 8 sin (16πt).

Therefore, the equation of the form y = A sin ωt that gives the distance of the mass from its rest position as a function of time is y = 8 sin (16πt).

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The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

The if statement evaluates the test expression inside the parenthesis ().

If the test expression is evaluated to true, statements inside the body of if are executed.

If the test expression is evaluated to false, statements inside the body of if are not executed.

The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

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In conditional statements, the part of the statement following 'if' is called the antecedent.

The antecedent is the condition that needs to be true for the consequent to occur.

The consequent is the part of the statement that follows 'then.'

An antecedent is a noun or pronoun that denotes a specific being, place, object, or clause.

It's also referred to as a referent. Without an antecedent, a sentence may be insufficient or nonsensical since it is

required to establish what or to whom a pronoun in a sentence is referring.

In summary, a conditional statement is structured as "if (antecedent) then (consequent)."

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The data type is quantitative data under the given condition that professor Donald creates a data set by combining student grades in his economics classes from the last 4 spring semesters.

Quantitative data is a type of data that deals with numbers and measurements. In the given case it deals with the attendance and the marks acquired by every individual in the course of 4 spring semesters.

Quantitative data is split  into two categories discrete and continuous.

Discrete variables are the ones that can only aquire one certain value, for instance  integers.

Continuous variables are the ones  that can aquire  any value within specified and certain range.

For the given case, the number of students who attended the class will fall under the example of discrete variables, while the scores on all components of the course as well as final grade would be examples of continuous variables.

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Answer:

s = 150f

Step-by-step explanation:

A tropical punch recipe calls for 300 ml of sugar for every 2 flavor packages. Write an equation that shows the relationship between s, the amount of sugar in milliliters, and f, the number of flavor packages for this recipe.

The amount of sugar in milliliters = s

The amount of flavor packages for these recipe = f

The relationship between 2 variables

= y ∝ x

y = kx

k = constant of proportionality

Hence:

s ∝ f

s = kf

Note ,

s = 300

f = 2

300 = 2k

k = 300/2

k = 150

Therefore, the equation that shows the relationship between s, the amount of sugar in milliliters, and f, the number of flavor packages for this recipe is:

s = kf

s = 150f

Answer:

2=150f

Step-by-step explanation:

khan said so

Answer:

Yes it is,

Step-by-step explanation:

Degree 1 (Exp 1) and it has 2 elements (2X and 1)

The cause-specific mortality rates per thousand for chronic conditions in the Bronx are (per thousand): Diabetes-related: 0.26,  Lung cancer: 0.44, Heart disease: 1.90 Asthma-related: 0.24.

To calculate the cause-specific mortality rate per thousand for chronic conditions in the Bronx, we divide the number of deaths from each specific condition by the total population and multiply by 1,000. By rounding the result to two decimal places, we can obtain the cause-specific mortality rate per thousand for each chronic condition of interest.

To calculate the cause-specific mortality rate per thousand for a particular chronic condition, we use the formula:

Mortality Rate = (Number of Deaths from the Condition / Total Population) * 1,000

Let's calculate the cause-specific mortality rates per thousand for each chronic condition based on the given figures:

Diabetes-related mortality rate:

(366 / 1,427,000) * 1,000 = 0.256 per thousand

Lung cancer mortality rate:

(633 / 1,427,000) * 1,000 = 0.443 per thousand

Heart disease mortality rate:

(2,711 / 1,427,000) * 1,000 = 1.898 per thousand

Asthma-related mortality rate:

(338 / 1,427,000) * 1,000 = 0.237 per thousand

Therefore, the cause-specific mortality rates per thousand for chronic conditions in the Bronx are approximately as follows:

Diabetes-related: 0.26 per thousand

Lung cancer: 0.44 per thousand

Heart disease: 1.90 per thousand

Asthma-related: 0.24 per thousand

These rates provide an indication of the number of deaths per thousand individuals in the population for each specific chronic condition of interest.

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The expression 4^3/2 is equal to 32 in exponentiation operation and  4√2 in division operation.

If the exponentiation operation (4^3) is performed before the division operation (/2), then the expression can be written as:

4^3/2 = (4^3) / 2

= (4 × 4 × 4) / 2

= 64 / 2

= 32

If the division operation (/2) is performed before the exponentiation operation (4^3), then the expression can be written as:

4^3/2 = 4^(3/2)

= 4^(1.5)

= 2 × 2 × 2^(0.5)

= 2 × 2 × √2

= 4√2

It's important to note that when dealing with expressions involving exponents, the order of operations matters and can significantly affect the resulting value.

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Answer:

4k + 13

Step-by-step explanation:

Base Expression: 8(2 - k) - 3(1 - 4k)

Step 1 - Distribution:

The values in the parenthesis must be simplified -

This is done simply by distributing the value in front of the parenthesis (8) into each of the values in the parenthesis (2 and -k).

The 8 is multiplied into the 2 giving us 16

The 8 is multiplied into the -k giving us -8k

Now we are left with 16 - 8k - 3(1 - 4k).

The same distribution must now be done on the other values in the parenthesis as well -

Again, the value in front of the parenthesis (-3) must be multiplied with the values inside the parenthesis (1 - 4k)

The -3 is multiplied into the 1 giving us -3

The -3 is multiplied into the -4k giving us 12k

Now our expression is 16 - 8k - 3 + 12k

For no reason other than simplicity, let's move the values around so they are easier to add and subtract:

16 - 8k - 3 + 12k  --->  16 - 3 + 12k - 8k

(no arithmatic is done here, but it is important to preserve the signs of all the values when moving them around)

From here we simply subtract the values to fully simplify the expression:

16 - 3 = 13

12k - 8k = 4k

4k + 13 is the final and most simplified expression of the original expression (without knowing the value for k)

P.S.: 13 + 4k is also technically correct, but, it's most often proper ettiquite (and often the simplest) to put more complex monomials (numbers) first in the expression.

Ex: 2x² + 6x + 8 rather than 8 + 2x² + 6x.

Hope this was comprehensive and helpful, good luck!

By using the concept of population standard deviation and sample standard deviation, it can be inferred that

2nd and 4th option  is correct

What is standard deviation?

At first, it is important to know about variance.

Variance is the sum of the square of deviation from the mean.

On taking the square root of the variance, standard deviation is obtained.

Here, the cases are

1) Population standard deviation \((\sigma)\) is known

2) Population standard deviation \((\sigma)\) is unknown

3) Sample standard deviation (s) is known

4) Sample standard deviation (s) is unknown

Now,

Formula for z

z = \(\frac{x - \mu}{\sigma}\) , \(\mu\) is the population mean, \(\sigma\) is the population standard deviation

Formula for t

t = \(\frac{x - \mu}{s}\) ,  s is the sample standard deviation

So if  Population standard deviation \((\sigma)\) is known and Sample standard deviation (s) is unknown, z table is used

If Population standard deviation \((\sigma)\) is unknown and Sample standard deviation (s) is known, t table is used

So 2nd and 4th option is correct

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Complete Question

The complete Question has been attached here

The polynomials have the value of k for

a) k = -2/3 and

b) k = 0 or k = 1.

The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).

For question a, having the polynomial x³ + kx² - 2kx + 1 the remainder is -2 when divided by x + 1.

so;

f(-1) = (-1)³ + k(-1)² - 2k(-1) + 1 = -2

-1 + k + 2k + 1 = -2 {collect like terms}

3k = -2 {divide through by 3}

k = -2/3

For question b, having the polynomial x² + x - 2, he remainder is -2 when divided by x + k

so;

f(-k) = (-k)² + (-k) - 2 = -2

k² - k - 2 = -2

k² - k = 2 - 2 {add 2 to both sides}

k(k - 1) = 0 {factorize}

k = 0 or k - 1 = 0

k = 0 or k = 1

Therefore, the value for k for the polynomial in question a is k = -2/3 and for question b, k = 0 or k = 1.

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Answer:

13.4

Step-by-step explanation:

Answer:

V = π r^2 h = π · 10^2 · 15 ≈ 4712.38898

Answer:

I also think 62 correct me if I'm wrong