what are the common factors of 20 and 30
A. 1,2,5,10
B. 1,2,10
C. 1,10
D. 1,5,10

Polynomials are  closed under the operations of addition, subtraction, and multiplication, polynomials constitute a system similar to that of integers.

Polynomial exponents are whole numbers.

The fact that addition is closed for the whole numbers ensures that the resultant exponents will also be whole numbers. Polynomials are hence closed under addition.

Polynomials will be closed under an operation if the operation produces another polynomial.

If we subtract 2 polynomials, the result is a polynomial. Therefore, they are also closed under subtraction.

Polynomials are an algebraic equation that has more than two terms, particularly the accumulation of numerous phrases that each include a different power of the same variable (s).

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Step-by-step explanation:

The divisor is the length of the vertical line

As the

fraction is

\(\sf \dfrac {Horizontal\:lines}{Vertical\:lines}\)

\(\boxed{\begin{minipage}{6 cm}\bf{\dag}\:\:\underline{\textsf{Fraction Rules :}}\\\\\bigstar\:\:\sf\dfrac{A}{B} + \dfrac{B}{C} = \dfrac{A+B}{C} \\\\\bigstar\:\:\sf{\dfrac{A}{B} - \dfrac{B}{C} = \dfrac{A-B}{C}}\\\\\bigstar\:\:\sf\dfrac{A}{B} \times \dfrac{C}{D} = \dfrac{AC}{BD}\\\\\bigstar\:\:\sf\dfrac{A}{B} + \dfrac{C}{D} = \dfrac{AD}{BD} + \dfrac{BC}{BD} = \dfrac{AD+BC}{BD} \\\\\bigstar\:\:\sf\dfrac{A}{B} - \dfrac{C}{D} = \dfrac{AD}{BD} - \dfrac{BC}{BD} = \dfrac{AD-BC}{BD}\\\\\bigstar \:\:\sf \dfrac{A}{B} \div \dfrac{C}{D} = \dfrac{A}{B} \times \dfrac{D}{C} = \dfrac{AD}{BC}\end{minipage}}\)

Answer:

it maybe 4 i am not sure

Step-by-step explanation:

Answer:

8, -8

Step-by-step explanation:

  Let's say that x is the larger number,

x - y = 16

y = x - 16

xy = P  where P is a minimum  

x(x-16) = P.  

(We can find the vertex, which is the minimum, by writing it in vertex format)  

  Completing square:  

x2 - 16x = P  

x2 - 16x + 64 = P + 64  

(x - 8)2 = P + 64.

 So,

x = 8 and -8

(8 - -8 -> 8 + 8 = 16)

Have a nice day!

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Step-by-step explanation:

1. 5+2+3=5+(2+3) 2. 9a is equivalent to 11a-2a 3. 7a + 04 - 2a is equivalent to 7a + -2a + 4 4. 8a-(8a-8) is equivalent or = to 8.

40

---

hope it helps

sorry if it doesn't

Answer:

1-19i

Step-by-step explanation:

In this scenario, we are dealing with a probability problem that involves  pharmaceutical and people. The pharmaceutical lab claims that 3% of patients experience negative side effects when taking a particular drug.

However, to confirm this, another lab randomly selects 10 PEOPLE who have taken the drug and wants to determine the expected number of people who experienced negative side effects.

To solve this problem, we can use the binomial distribution formula, which states that the probability of x successes in n trials is given by:

P(x) = (nCx) * p^x * q^(n-x)

Where nCx is the binomial coefficient, p is the probability of success, q is the probability of failure (1-p), and x is the number of successes.

In this case, n = 10, p = 0.03, and q = 0.97 (since the drug causes negative side effects in 3 out of 100 patients, or 0.03). To find the expected number of people who experienced negative side effects, we can simply multiply the number of trials (n) by the probability of success (p):

Expected number of people = n * p
Expected number of people = 10 * 0.03
Expected number of people = 0.3

Therefore, we can expect that 0.3 (or 3 out of 10) of the randomly selected patients experienced negative side effects from the drug. It's important to note that this is only an expected value and does not guarantee that exactly 3 patients will experience negative side effects. The actual number may vary.

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A total of 8,000,000 seven-digit phone numbers that can be formed if the first digit cannot be 0 or 1 and one digit can be repeated.

There are 8 possible choices for the first digit (2-9), and each of the other six digits can have 10 possible choices (0-9). Therefore, 8 x 10 x 10 x 10 x 10 x 10 x 10 = 8,000,000 possible seven-digit phone numbers.

To better understand this, let's break it down further. For the first digit, there are 8 possible choices since 0 and 1 are not allowed. For the second digit, there are 10 possible choices since any digit (0-9) can be used. For the third digit, there are 10 possible choices again since any digit (0-9) can be used.

The same holds true for the fourth, fifth, sixth, and seventh digits, giving us 8 x 10 x 10 x 10 x 10 x 10 x 10 = 8,000,000 seven-digit phone numbers.

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The possible triangle orientations are given below -

The relation is that the sum of the two sides of the triangle is greater than the third side. Mathematically -

a + b > c

Given are the sides of a triangle as shown in the triangle.

{ 1 } -

2 yd , 7 yd , 8 yd

7 + 2 > 8

9 > 8    {true}

It forms a triangle.

{ 2 } -

1.5 cm, 2.3 cm, 3.8 cm

2.3 + 1.5 > 3.8

3.8 > 3.8    {false}

It does not form a triangle.

{ 3 } -

3 in. , 4 in. , 5in.

4 + 3 > 5

7 > 5  {true}

It forms a triangle.

{ 4 } -

5 m , 9 m , 14.5 m

9 + 5 > 14.5

14 > 14.5   {false}

It does not form a triangle.

{ 5 } -

14 ft , 15.8 ft , 33 ft

15.8 + 14 > 33

29.8 > 33    {false}

It does not form a triangle.

{ 6 } -

2.8 mm , 7.1 mm , 9.5 mm

7.1 + 2.8 > 9.5

9.9 > 9.5 {true}

It forms a triangle.

Therefore, the possible triangle orientations are given below -

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Answer:

4

Step-by-step explanation:

( -4, 10)    (-8, -6)

slope = y / x

From -8 to -4 it translates 4 units to the right.

From 10 to -6 it translates 16 units down.

16 / 4 = 4

Answer:

The gradient/slope of the line is 4.

Step-by-step explanation:

(x₁, y₁)=(-4, 10)   (x₂, y₂)=(-8, -6)

Plug into the formula of Δy/Δx which is y₂-y₁/x₂-x₁

-6-10/-8-(-4)

-6-10= -16

-8-(-4)= -4

-16/-4 = 4

The gradient/slope of the line is 4.

Hope this helped. If you require further assistance from me, please comment below.

The milliliters of liquid veterinarian gave for 8 milliliters of drug rather than 2 is approximately equal to 25.6 milliliters of liquid

The liquid-to-drug ratio is equal to 3.2

If the veterinarian wants to administer 8 milliliters of the drug instead of 2 milliliters,

Let 'x' milliliters be the required volume of the liquid needed for this dosage.

The liquid-to-drug ratio of 3.2 means that for every 3.2 milliliters of liquid, there is 1 milliliter of the drug.

This implies, to find the volume of the liquid needed for 8 milliliters of the drug,

Set up a proportion,

(3.2 mL liquid / 1 mL drug) = (x mL liquid / 8 mL drug)

Cross-multiplying, we get,

⇒ 3.2 mL liquid × 8 mL drug = 1 mL drug × x mL liquid

⇒ 25.6 mL liquid = x mL liquid

Therefore, the veterinarian would need to administer approximately 25.6 milliliters of liquid in order to deliver 8 milliliters of the drug, based on the given liquid-to-drug ratio.

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The conclusion "A > (K > J)" is proved using a conditional proof based on the given premises.

To prove the conclusion "A > (K > J)" from the given premises, we can use a conditional proof. Here's a step-by-step breakdown of the proof:

1. Assume A as the temporary assumption. (Assumption)

2. From premise 1, we have: A > (K > L).

3. Assume K as the temporary assumption. (Assumption)

4. From assumption 3 and premise 2, we have: (L v N) > J.

5. From assumption 3, premise 2, and the disjunction elimination (vE) rule, we have two cases to consider:

  a) Assume L as the temporary assumption. (Assumption)

     - From assumption 4, we have: J. (Direct derivation)

  b) Assume N as the temporary assumption. (Assumption)

     - Since N is arbitrary and has not been used, we can conclude anything from this assumption. For the sake of simplicity, let's conclude J. (Direct derivation)

6. In both cases (5a and 5b), we have J as the result.

7. Based on cases 5a and 5b, we can conclude (K > J) using the conditional introduction (>) rule.

8. From assumption 3 and the derived result in step 7, we have K > J.

9. Based on assumption 3 and the derived result in step 8, we can conclude (A > (K > J)) using the conditional introduction (>) rule.

10. Since the assumption in step 3 was arbitrary, we can discharge it and conclude (A > (K > J)).

11. Since the assumption in step 1 was arbitrary, we can discharge it and conclude that if A holds, then (K > J) follows, i.e., A > (K > J). (Conditional proof)

Therefore, we have proved the conclusion "A > (K > J)" using a conditional proof based on the given premises.

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150 is not a required term for this proof, thus it is not included in the answer.

Given premises:

1. A > (K > L)2. (L v N) > J Conclusion: A > (K > J)Proof:

Assume A is true. This is our assumption for the Conditional proof. Now we need to prove that (K > J) will also be true with the given premises.So, from 1: A > (K > L) with A assumed to be true, we can infer:(K > L) (using Conditional Elimination) Now we need to prove that K > J. So assume K to be true to show that J will be true as well. So, for this assumption, we have to prove L also to be true. From (K > L), with the assumption that K is true, we can conclude that L is also true. Now we can use this result to prove the final statement:

(L v N) > J (Premise 2) (using Conditional Elimination)Since we have proved that L is true, we can conclude that J is true as well. We have used the premise 2 to make this conclusion. Hence the conclusion follows:A > (K > J) is true.150 is not a required term for this proof, thus it is not included in the answer.

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From the stem and leaf plot, let's write the data set:

10.9 cm

11.0 cm

11.2 cm

11.2 cm

12.1 cm

12.3 cm

We need to find the range of the data set, which is, the difference between the length of the longest pencil and the shortest pencil.

From the data set, we can see:

• Length of Longest Pencil = 12.3 cm

• Length of Shortest Pencil = 10.9 cm

The difference is

12.3 - 10.9 = 1.40 cm

The probability that the Davis boys will occupy the first two seats in the row, the Jones boys will occupy the next three seats, and the Smith boys will occupy the last four seats is 7.937×\(10^{-4}\).

There are \(\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]\) potential arrangements for the nine boys if we do not make a distinction amongst boys with the same last name. We are curious in the likelihood of a specific one of these configurations.

Probability = \(\frac{1}{\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]}\)

                  = \(\frac{2!3!4!}{9!}\)

                 = 0.0007937

                = 7.937×\(10^{-4}\)

Hence, the probability is 7.937×\(10^{-4}\).

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Answer:

2. absolute value of p - q

Explanation:

Because when you calculate distance, you always use absolute value.

Can I get a thx and brainliest?

Answer:

Step-by-step explanation:

Using binomial distribution,

\(p=\left(\begin{array}{c} 8\\ 6\end{array}\right)*(\dfrac{1}{2} )^6*(\dfrac{1}{2} )^2\\\\\\=\dfrac{8*7*6*5*4*3}{6*5*4*3*2*1} *\dfrac{1}{256} =\dfrac{28}{256} =\dfrac{7}{64} \\\\\)

(a) The air volume in the chamber at the surface can be calculated using the ideal gas law, which states that the product of pressure and volume is proportional to the number of moles and temperature of the gas.

At the surface, the pressure is 1.00 atm, and assuming the air inside the chamber is at the same temperature as the surface (15.4°C or 288.55 K), we can use the ideal gas law equation:

PV = nRT,

where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Rearranging the equation, we have:

V = (nRT) / P.

Substituting the given values, n = number of moles of air, R = ideal gas constant (8.314 J/(mol·K)), P = 1.00 atm, and T = 288.55 K, we can calculate the air volume in the chamber at the surface.

(b) If air had not been released from the tanks, the air volume in the chamber at depth h = 88.0 m can be determined using the same approach as in part (a). However, we need to consider that the pressure at that depth is different from the surface pressure.

The pressure at depth is given by the equation p = p0 + ρgh, where p0 = 1.00 atm is the surface pressure, ρ = 1030 kg/m³ is the density of seawater, g = 9.8 m/s² is the acceleration due to gravity, and h = 88.0 m is the depth. By substituting these values into the equation and using the ideal gas law, we can calculate the air volume in the chamber at that depth.

(c) To maintain the original air volume in the chamber as it descends, air needs to be released from the tanks to equalize the pressure inside the chamber with the external water pressure. The number of moles of air that needs to be released can be calculated by considering the change in pressure and using the ideal gas law.

The difference in pressure is given by ΔP = p - p0, where p is the pressure at depth and p0 is the surface pressure. By rearranging the ideal gas law equation as ΔP = (nRT) / V and solving for n, we can determine the number of moles of air that needs to be released.

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All the inequalities below do not have a solution as there variables do not exists after simplification.

Inequality, When two integers or algebraic expressions are said to be larger than, greater than or equal to, less than, or less than or equal to each other in sequence. Inequalities can be stated as either statements of fact in the form of theorems, which are solved using methods similar to those used to solve equations, or as questions. For instance, the triangle inequality asserts that the length of the remaining side is more than or equal to the sum of the lengths of any two sides of a triangle. Several of these inequalities, including the Cauchy-Schwarz inequality, are used in the proofs of many of mathematical analysis' most significant theorems.

The given equation is:

4s + 6 ≥ 6 + 4s

Rearranging the following we have:

4s - 4s ≥ 6 - 6 = 0

The inequality has no solution.

b. 3r + 5 > 3r − 2

Also has no solution as the variable is cancelled.

c. Similarly, for the third equation there exists no solution.

Hence, all the inequalities below do not have a solution as there variables do not exists after simplification.

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General equation for slope-intercept form

y = mx+c

comparing the given eqn with this ,

m= slope = 2

Answer:

So the sequence of the five numbers are;

10,26,74,218,650

Step-by-step explanation:

In this question, we are interested in building a sequence of 5 numbers given the initial term.

Okay, to build this sequence, we will need to look at the rule that guides the building of the new sequence:

The rule is that the next term is 4 less than 3 times the previous term.

Okay, let’s call the next term y, while the previous term is x.

Following what was specified in the question;

y = 3x -4

Recall; the next term(y) is 4 less (-4) than 3 times (3 multiplied by) the previous term (x)

So let’s start with the initial term of 10.

The next term will be;

y = 3(10) -4 = 30-4 = 26

The next term after 26 will be ;

y = 3(26) -4 = 78-4 = 74

The next term after 74 will be;

y = 3(74) -4 = 222-4 = 218

The next term after 218 will be;

y = 3(218) -4 = 650

The sampling method described in the scenario is d. stratified sampling.

In stratified sampling, the population is divided into distinct subgroups or strata based on certain characteristics or variables. The researcher then randomly selects samples from each stratum in proportion to their representation in the population. This approach ensures that the sample is representative of the population's diversity.

In this case, the researcher has divided the population of teachers into two strata: male teachers and female teachers. By randomly selecting 50 male teachers and 50 female teachers, the researcher is ensuring that both genders are represented in the sample.

The researcher's intention is to have a sample that reflects the gender distribution of teachers in the population accurately. Therefore, stratified sampling is the appropriate method in this scenario.

Other sampling methods, such as systematic sampling, convenience sampling, random sampling, and cluster sampling, are not applicable because they do not specifically address the need to ensure proportional representation of genders in the sample.

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Answer:

Step-by-step explanation:

What are u asking for x or y

Answer:

1 = B, 2 = B, 3 = C

Step-by-step explanation:

1) When there are same digits with exponents being multiplied, you add the exponents

2) When an exponent is being distributed through a parenthesis, you multiply

3) When there are same digits with exponents being divided, you subtract the exponents

The result of subtracting the polynomials (6x2 – X + 8) – (x2 + 2) is 5x^2 – x + 6

The subtraction of the polynomials is given as:

(6x2 – X + 8) – (x2 + 2) =

Rewrite the above expression properly as:

(6x^2 – x + 8) – (x^2 + 2) =

The next step is to open the brackets.

Start by opening the first bracket (here the signs remain the same)

6x^2 – x + 8 – (x^2 + 2) =

Next, we open the second bracket (here the sign changes, because of the minus outside the bracket)

So, we have;

6x^2 – x + 8 – x^2 - 2 =

Next, we collect the like terms

6x^2 – x^2 – x + 8  - 2 =

Subtract x^2 from 6x^2

5x^2 – x + 8  - 2 =

Subtract 2 from 8

5x^2 – x + 6

Hence, the result of subtracting the polynomials (6x2 – X + 8) – (x2 + 2) is 5x^2 – x + 6

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Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

Answer:

Unit price = 4.96/16 = 0.31

$0.31

Step-by-step explanation:

The unit price of the turkey is $0.13

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given;

Price of package of sliced turkey=$4.96

Number of slices in package= 16

Unit price= price of package/number of slices in package

               =4.96/16

               =0.31

Therefore, the value of each slice will be $0.13

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Answer:

42

Step-by-step explanation:

6 x 6 is 36. 3 x 2 is 6. 36 + 6 is 42.

To the nearest ten dollars, there would be approximately $81,329 in the account after 11 years.

To calculate the future value of an investment with compound interest, we can use the formula:

FV = P(1 + r/n)^(nt)

Where:

FV = Future value

P = Principal amount (initial investment)

r = Annual interest rate (as a decimal)

n = Number of times interest is compounded per year

t = Number of years

In this case:

P = $60,000

r = 3.4% = 0.034 (as a decimal)

n = 365 (daily compounding)

t = 11 years

Plugging in these values, we can calculate the future value (FV):

FV = $60,000 * (1 + 0.034/365)^(365*11)

Calculating this expression, we find:

FV ≈ $60,000 * (1.000093835)^40015 ≈ $81,329.20

Therefore, to the nearest ten dollars, there would be approximately $81,329 in the account after 11 years.

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