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Please find one news article related to a current, specific U.S. trade barrier issue. (within the past 4 weeks)

Binomials include formulas such as a + b, x - y, etc. For the expansion of a binomial raised to exponents 2 and 3, we have a set of algebraic identities. Examples are (a + b)2 = a2 + 2ab + b2.

Let us review the definition of a "binomial" before understanding the formulas for binomial expansion. An expression in algebra with two terms is called a binomial.

Binomials include formulas such as a + b, x - y, etc. For the expansion of a binomial raised to exponents 2 and 3, we have a set of algebraic identities. Examples are (a + b)2 = a2 + 2ab + b2.

However, what happens if the exponents are larger numbers? The expansion can be difficult to locate manually.

This procedure is made simpler using the binomial expansion formula. Learn the formula for the binomial expansion and a few examples with solutions.

The expansion of (a + b)3 can be found in Example 1.

Solution:

The sum of (a plus b)3

by applying the binomial expansion formula,

(x + y)n = nC 0 xn y0 + nC 1 xn-1 y1 + nC 2 xn-2 y2 + nC 3 xn-3 y3 +... + nC n 1 x yn-1 + nC n x0yn

(a + b)

3 = 3C

0  a3 + 3C

1  a(3 - 1) (3 - 1) b + 3C

2  a(3 - 2) (3 - 2) b2 + 3C

3  a(3 - 3) b3

= ( 3! / [(3-0)!0!] ) a3 + ( 3! / [(3-1)!1!] ) a(3 - 1) (3 - 1) b + ( 3! / [(3-2)!2!] ) a(3 - 2) (3 - 2) b2 + ( 3! / [(3-3)!3!] ) a(3 - 3) b3

= (a3 first) + (a2 second) + (a1 second) + (a0 third)

= a3 + 3 a2, b + 3 a b2, and b3

(A + B)3 = A3 + 3 A2 B + 3 A B 2 + B3.

The Complete Question.

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True, the general form of a large-sample 100% confidence interval for a population proportion p is where is the sample proportion of observations with the characteristic of interest.

The general form of a large-sample 100% confidence interval for a population proportion p is given by the formula:

p ± z(standard error of p)

where p is the sample proportion of observations with the characteristic of interest and z is the critical value from a standard normal distribution corresponding to the desired level of confidence (e.g. z = 1.96 for a 95% confidence interval). The standard error of p is calculated as the square root of (p(1-p)/n), where n is the sample size.

This formula is based on the central limit theorem and the assumption that the sample is random and large enough (n > 30). In this case, the distribution of p is approximately normal and the confidence interval provides a range of plausible values for the true population proportion.

Correct Question :

The general form of a large-sample 100% confidence interval for a population proportion p is where is the sample proportion of observations with the characteristic of interest. True or false.

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The probability that your box is a winner is 1/10,000,000.

The probability that your box is a winner can be calculated as the probability of a box rattling and being a winner, divided by the probability of a box rattling.

P(Winner | Rattle) = 1/1,000,000

P(Rattle) = 1/100

P(Winner) = P(Winner | Rattle) * P(Rattle)

= (1/1,000,000) * (1/100)

= 1/10,000,000

a. The expected number of points after one roll is the average of the possible outcomes, which are 1, 2, 3, 4, 5, and 6.

The average is (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5.

b. The expected number of points after two rolls is the average of the possible outcomes of the sum of two rolls.

For example, the possible outcome of 2 rolls could be (1,1), (1,2), (1,3), ..., (6,6).

The average of these 36 possible outcomes is 7.

c. The expected number of points after 100 rolls is the average of the possible outcomes of the sum of 100 rolls, which would be approximately 350.

This is because the expected value for each roll is 3.5, and for 100 rolls it would be 100 * 3.5 = 350.

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The area under the curve between z = −2.0 and z = −1.0 is 0.1359.

We can use tables to find the area under the normal curve between two values of z.

However, tables give areas from z = 0 to z = 3.9 (beyond which there is literally no change). But as the normal curve is symmetric at z = 0, we can use it to find between any two given z values.

For example, for the area under the curve between z = −2.0 and z = −1.0, we can take values for z = 2.0 and z = 1.0; their difference will give the area between z = −2.0 and z = −1.0.

From tables for z = 1.0, we have 0.8413 and for z = 2.0, we have 0.9772 and

Hence, the Area under the curve between z = −2.0 and z = −1.0 is 0.9772−0.8413 = 0.1359.

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The temperature at which the rate constant becomes five times greater than the rate constant at 275 K is 325 K.

Let's say that temperature is represented by t and the rate constant is represented by r.

Let' say r₁ = R, r₂ = 3R, t₁ = 275 K and t₂ = 300 K.

considering the relationship between rate constant and temperature is linear.

t - 300 = [(300 - 275)/(3R - R)](r -  3R)

t - 300 = (25/2R)(r - 3R)

We are asked to determine the temperature at which the rate constant becomes five times greater than the rate constant at 275 K.

t - 300 = (25/2R)(5R - 3R)

t - 300 = (25/2R)(2R)

t - 300 = 25

t = 325 K

Hence, the temperature at which the rate constant becomes five times greater than the rate constant at 275 K is 325 K.

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Answer:

4:3

Step-by-step explanation:

1m = 100cm

75cm = 75cm

ratio of 1m:75cm

(100cm:75cm)÷25 = 4:3

so 1m:75cm = 4:3

Answer:

(-5, 0)

Step-by-step explanation:

Answer:

D (-5,0)

Step-by-step explanation:

OOOOOOOOOOOOOOOOOOOOOOOO

To compute the median of three sets of scores, we need to arrange the scores in order from smallest to largest and then select the middle score.

Mean, median and mode are measures of central tendency and are used to describe the central value of a set of data. The mean is the average of all the values in the set, the median is the middle value and the mode is the most frequently occurring value.

To compute the mean of three sets of scores, we need to sum up all the scores and divide by the total number of scores. This can be represented by the formula:

Mean = (Score1 + Score2 + Score3) / 3

To compute the median of three sets of scores, we need to arrange the scores in order from smallest to largest and then select the middle score. This can be represented by the formula:

Median = (Score2 + Score3) / 2

To compute the mode of three sets of scores, we need to identify the score that occurs the most frequently. This can be represented by the formula:

Mode = Most Frequently Occurring Score

For example, if the three scores are 3, 7, and 4, then the mean is (3 + 7 + 4) / 3 = 4.67, the median is (3 + 4) / 2 = 3.

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Answer:

a) Since the question is asking for a disjunction, involving an or, this means that the answer to the question can be either solution, not both.

b) Conjunction involves an "and" so it means both answers

Step-by-step explanation:

[tex]3 \sqrt{13} [/tex]

Answer:

y = 17

Step-by-step explanation:

the absolute value always gives a positive value , that is

| - a | = | a | = a

given

y = | x | + 10 ( substitute x = - 7 into the equation )

y = | - 7 | + 10 = | 7 | + 10 = 7 + 10 = 17

Answer:

[tex]m\angle A = 44\textdegree, a = 13.9, b = 18.0[/tex]

Step-by-step explanation:

Step 1: Solve for the Missing Angle

The measures of all of the interior angles of a triangle will always add up to [tex]180\textdegree[/tex]. Therefore,

[tex]m\angle A = 180\textdegree - (m\angle B + m\angle C) = 180\textdegree - (64\textdegree + 72\textdegree) = 44\textdegree[/tex]

Step 2: Solve for the Missing Sides

When we are given the side lengths and angle measures of a triangle, we can use either the Law of Sines or the Law of Cosines to solve for the rest of the triangle.

The Law of Sines is as follows: [tex]\frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c}[/tex]

The Law of Cosines is as follows: [tex]c^{2} = a^{2} +b^{2} -2abcosC[/tex] (you can exchange c for a or b, respectively)

In this case, we are only given 1 side length and all 3 angle measures, so it would be more appropriate to use the Law of Sines as we need at least 2 side lengths to use the Law of Cosines.

Now that we know which formula to use, let's start by solving for [tex]a[/tex], using the given values of [tex]c=19[/tex], [tex]\angle A = 44\textdegree[/tex], and [tex]\angle C = 72\textdegree[/tex].

Substituting these values in, we get:

[tex]\frac{sinA}{a} = \frac{sinC}{c} \\ \frac{sin44\textdegree}{a} = \frac{sin72\textdegree}{19}\\a=\frac{19sin44\textdegree}{sin72\textdegree} \approx \bf 13.9[/tex]

Repeating this process for [tex]b[/tex], this time using [tex]\angle B = 64\textdegree[/tex], we get:

[tex]\frac{sinB}{b} = \frac{sinC}{c} \\ \frac{sin64\textdegree}{b} = \frac{sin72\textdegree}{19}\\b=\frac{19sin64\textdegree}{sin72\textdegree} \approx \bf 18.0[/tex]

The quotient of the division is  x^3 - 2x^2 + 4x - 8

From the question, we have the following parameters that can be used in our computation:

quotient of (x4 − 3x3 + 6x2 − 12x + 8) ÷ (x − 1)?

Using the long division method of quotient, we have

x - 1 | x^4 - 3x^3 + 6x^2 - 12x + 8

The division steps are as follows

          x^3 - 2x^2 + 4x - 8

x - 1 | x^4 - 3x^3 + 6x^2 - 12x + 8

        x^4 - x^3

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

             -2x^3 + 6x^2 - 12x + 8

             -2x^3 + 2x^2

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

                         4x^2 - 12x + 8

                         4x^2 - 4x

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

                                       -8x + 8

                                       -8x + 8

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

Hence, the quotient is  x^3 - 2x^2 + 4x - 8

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Answer:

13 7/12

Step-by-step explanation:

5+7+13

4/12+3/12+7/12

Answer: [tex]\displaystyle 2x^4 + 9x^3-8x^2+9x -13[/tex]

Step-by-step explanation:

     Given:

[tex]\displaystyle (2x^4 + 9x^3 -8)-(8x^2-9x+5)[/tex]

     Subtract the second term:

[tex]\displaystyle (2x^4 + 9x^3 -8)-8x^2+9x-5[/tex]

     Reorder by the power's degree:

[tex]\displaystyle 2x^4 + 9x^3-8x^2+9x -8-5[/tex]

     Combine like terms:

[tex]\displaystyle 2x^4 + 9x^3-8x^2+9x -13[/tex]

Answer:

z=12.25

Step-by-step explanation:

first we are going to find the hypotenus x

of the first part of the tiangle as shown in my diagram, using the Pythagoras rule-

hyp= x

opp= 15

adj=5

thus hypothenus²=opposite²+adjacent²

x²=15²+5²

x²=225+25

x²=250

the you use √ to find x

√x²=√250

x=15.81

step 2= to find z

hyp=20

opp:z

adj:15.81

hyp²=opp²+adj²

20²=z²+15.81²

400=z²+250

z²+250=400

z²=400-250

z²=150

√z²=√150

z=12.25

Answer:

z ≈ 12.2 cm

Step-by-step explanation:

using Pythagoras' identity in the 2 right triangles.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

consider the right triangle on the left

let the third side, the hypotenuse be x , then

x² = 5² + 15² = 25 + 225 = 250

consider the right triangle on the right , then

x² + z² = 20²

250 + z² = 400 ( subtract 250 from both sides )

z² = 150 ( take square root of both sides )

z = [tex]\sqrt{150}[/tex] ≈ 12.2 cm ( to 1 decimal place )

The solution to the equation is x = 27

From the question, we have the following parameters that can be used in our computation:

√2x+10 -6=2

Add 6 to both sides of the equation

This gives

√2x+10 = 8

Square both sides

So, we have the following representation

2x + 10 = 64

Subtract 10 from both sides

2x = 54

Divide by 2

x = 27

Hence, the solution is 27

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a) The expressions are given as follows:

b) The will be at the same altitude at a time of: 44 seconds.

The situation is modeled by linear functions in slope-intercept format, as follows:

y = mx + b.

In which:

Hence the functions are defined as follows:

The planes will have the same altitude when:

A(t) = B(t)

Hence:

800 + 15t = 360 + 25t

10t = 440

t = 44 seconds.

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Answer:

the answer to this question is 6:00

The number of patients before 2 hours is 40,000.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.

As per the given data:

The growth rate of covid patients is given and number of patients at 8:00 am is 44,100.

We have to find out what was the number before 2 hours.

Growth rate (G) = 5% per hour.

Number of patients at 8 : 00 AM = 44,100

Let's assume the number of patients 2 hours before is P.

Patients after two hours:

P(1 + G/100)^2

= P(1 + 5/100)^2

= P(1.05)^2

= 1.1025P

From the given data:

1.1025P = 44,100

P = 40,000

The number of patients before 2 hours is 40,000.

Hence, The number of patients before 2 hours is 40,000.

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Meta-analysis is a set of qualitative statistical techniques used to combine the results of multiple, independent research events to arrive at a summary statement about the data.

It is used to identify patterns across studies and to synthesize the results from different studies into a coherent and comprehensive interpretation of the research results. Meta-analysis is commonly used in medical research to identify treatments that are most effective, as well as in social sciences to determine the impact of a policy or program on a population.

Meta-analysis is also used to compare different theories and studies, to evaluate the strength of studies, and to identify any gaps in the existing research. By combining data from multiple studies, meta-analysis can provide a more robust and accurate summary of the effects of a particular intervention or program.

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Answer:

To find the lowest common multiple (LCM) of 1080, 1188, and 1815, we need to find the smallest number that is a multiple of all three numbers.

One way to find the LCM is to use prime factorization. We can prime factorize each number and then multiply the highest exponent of each prime factor to get the LCM.

1080 = 2^4 * 3^3

1188 = 2^2 * 3 * 199

1815 = 5 * 11 * 163

The LCM is:

2^4 * 3^3 * 5 * 11 * 163 = 1080 * 11 * 163

So the LCM of 1080, 1188, 1815 is 207940.

Answer:

Jimmy spent 4/25 of his $5,000 budget on hotel accommodation, which is equal to $2,000. He spent 3/20 of his budget on airfare, which is equal to $1,500, 1/10 of his budget on shopping, which is equal to $500, and 1/5 of his budget on the remainder, which is equal to $1,000. This means that Jimmy spent $2,000 on hotel accommodation, which is $500 more than he spent on food.

The table of x, y and t for the given parametric equations is

The Table is as follows:

t     -4    -2    0    2    4

x    16    4    0    4    16

y      0    2    4    6    8        

The parametric equations are given:

x = t², y = t + 4; -4 ≤ t ≤ 4

if t = -4

x = (-4)² = 16

y = -4 + 4 = 0

if t = -2

x = (-2)² = 4

y = -2 + 4 = 2

if t = 0

x = (0)² = 0

y = 0 + 4 = 4

if t = 2

x = (2)² = 2

y = 2 + 4 = 6

if t = 4

x = (4)² = 16

y = 4 + 4 = 8

The Table is as follows:

t     -4    -2    0    2    4

x    16    4    0    4    16

y      0    2    4    6    8  

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Answer:

The equation 2n + 1 = 157 represents the situation where the sum of two consecutive numbers is 157.

To find the first number, we can start by subtracting 1 from both sides of the equation:

2n = 156

Then we can divide both sides by 2:

n = 78

So the first number is 78, which corresponds to the answer choice B.

Step-by-step explanation:

1. The 08 08 bus takes 89 minutes to go from Birmingham to Coventry

2. The latest time Chris have to leave his house is 7:26

The bus time table shows that only two buses will leave can meet up with Chris resuming time. The bus 7:05 and the bus that leave by 7: 33

Calculating the latest time Chris could leave his home is by taking the second bus.

7 minutes to walk from his house to his bus stop. Therefore the 7minutes is deducted from the starting time of the second bus.

7:33-7minutes = 7: 26 am

Therefore the latest time he should leave home to meet up with 9:30 am resuming is 7:26 am

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To identify the initial amount (a) and rate of growth in the equation y=100000(1.09)^3, you can use algebra to isolate the variables.

First, divide both sides of the equation by 100000 to get y/100000=(1.09)^3. Then, take the cube root of both sides of the equation to get y/100000=1.09.

Finally, multiply both sides of the equation by 100000 to get y=109000. Therefore, the initial amount (a) is 100000, and the rate of growth is 1.09.

The initial amount, also known as the starting point or the base value, is the value of a variable at the beginning of a given period.

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Drake uses 9/4 cup of sugar to make 9 mug of brownie. Then the amount of sugar needed to make one brownie is 1/4 cup of sugar.

Determine how much sugar is needed

These are the specified parameters:

9/4 cup of sugar to make 9 mug of brownie.

Determine much sugar to make one brownie

Lots of sugar = cup of sugar : mug of brownie

                      = 9/4 : 9

                      = 9/4 × 1/9

                       = 1/4

So the amount of sugar needed to make one brownie is 1/4 cup of sugar.

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Answer:

-2

Step-by-step explanation:

Δy =4- (-8) =12

Δx = -4 -2 = -6

12/(-6) =-2

The total number of micrograms present in the 65.3 kilograms is equal to 65,300,000,000 micrograms.

Conversion of units from kilogram to grams is :

1 kilogram = 1,000 grams

Conversion of units from grams to micrograms is :

1 grams  = 1,000,000 micrograms

⇒ 1 kilogram = ( 1,000 × 1,000,000 ) micrograms

⇒1 kilograms = 1,000,000,000 micrograms

Substitute the required value for the converting kilogram to micrograms we get,

⇒ 65.3 kilograms = ( 65.3 × 1,000,000,000 ) micrograms

⇒65.3 kilograms = 65,300,000,000 micrograms

Therefore, the total quantity of micrograms in 65.3 kilograms is equal to 65,300,000,000 micrograms.

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