A rectangular room is 5 meters longer than it is wide, and it’s perimeter is 26 meters. Find the dimension of the room

The fifth term of the expansion by using Binomial Expansion is +1008x¹⁵y¹⁴.

When algebraic identities cannot be employed to extend a binomial, the binomial expansion formulae are used to determine the powers of the binomials.

The expansion of (x + y)^n is given by this binomial expansion formula, where n is a natural number. There are (n + 1) terms in the expansion of (x + y)^n.

Given that:

[tex]=(\dfrac{1}{2}x^3y^2-4y)^9[/tex]

Use the binomial expansion theorem to find each term. The binomial theorem states [tex](a+b)^n = \sum \limits^n_{k=0}nCk*(a^{n-k}b^k)[/tex]

[tex]\sum \limits^9_{k=0} \dfrac{9!}{(9-k)!k!}* (\dfrac{1}{2}*(x^3y^2))^{9-k}*(-4y)^k[/tex]

Expand the summation.

[tex]=\dfrac{9!}{(9-0)!0!}*(\dfrac{1}{2}*(x^3y^2)^{9-0}*(-4y)^0+ \dfrac{9!}{(9-1)!1!}*(\dfrac{1}{2}*(x^3y^2)^{9-1}*(-4y)^1+...+\dfrac{9!}{(9-9)!9!}*(\dfrac{1}{2}*(x^3y^2)^{9-9}*(-4y)^9[/tex]

Simplify the exponents for each term of the expansion.

[tex]=1*(\dfrac{1}{2}*(x^3y^2)^{9}*(-4y)^0+ 9*(\dfrac{1}{2}*(x^3y^2)^{8}*(-4y)^1+...+1*(\dfrac{1}{2}*(x^3y^2)^{0}*(-4y)^9[/tex]

Simplify the polynomial result.

[tex]=\dfrac{x^{27}y^{18}}{512}-\dfrac{9x^{24}y^{17}}{64}+\dfrac{9x^{21}y^{16}}{2}-84x^{18}y^{15}+1008x^{15}y^{14}-8064x^{12}y^{13}+43008x^9y^{12}-147456x^6y^{11}+294912x^3y^{10}-262144y^9[/tex]

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Answer:

Yes, these system of inequalities do have solutions. The solutions for y> 3x+ 14  would be contained in region B and C and the solutions for y<3x+2 would be in regions B and A. Therefore, the answer is region B.

Step-by-step explanation:

If you graphed y> 3x+ 14, you would see that the right side of the coordinate grid would be left blank and empty while the left side would be colored within a dotted line which would be y=3x+ 14. We will call those regions B and C. When you graph y<3x+2 you would see that this time the left side of the coordinate grid would be left blank and the right would be colored in. If you then graph both y> 3x+ 14 and y<3x+2 you would see that only region B is left blank. Therefore, region B would be the solutions for the system of the two inequalities.

Answer: 35 is 70% of 50

Step-by-step explanation:

Steps to solve "35 is 70 percent of what number?"

We have, 70% × x = 35

or,

70

100

× x = 35

Multiplying both sides by 100 and dividing both sides by 70,

we have x = 35 ×

100

70

x = 50

If you are using a calculator, simply enter 35×100÷70, which will give you the answer.

Answer:

50

Step-by-step explanation:

35 + 15 = 50

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

15 is 30% of 50 There fore 50 is the correct answer

I took this exam, its the 5.08 Ratios and rates practice exam right?

Have an amazing Day and good luck (:

The surface area of the right prism is equal to 142 square inches.

Herein we find the case of a right prism with a rectangular base, of which we need to determine its surface area (A), in square inches, that is the sum of the areas of all faces. The surface area is the sum of areas of rectangles, whose formula is:

A = w · l

Where:

Now we proceed to determine the surface area of the rectangular prism:

A = 2 · (7 in) · (3 in) + 2 · (5 in) · (7 in) + 2 · (3 in) · (5 in)

A = 42 in² + 70 in² + 30 in²

A = 142 in²

The right prism has a surface area of 142 square inches.

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The linear speed is 141.37ft/min.

The relation between the linear speed v and rotational speed (ω) is given by the relation

v=rω.

we know that rotational speed is the speed with which we measure rotations. So

ω=Number of Rotations/Time in minutes.

linear speed:

v=2πrn/T

Linear speed is defined as the wheel would have traveled, had it been rolling on a flat surface.

The given information is the revolution speed of the Ferris wheel as 1 revolution in 8 min.

we can observe that if the wheel rotates one full revolution, the distance that it covers is equal to the circumference of the wheel. In one revolution the distance it travels is

2*π*(180)

distance=1130.9733 ft.

Also, it takes 8 min to complete the distance. so the linear speed is

speed=distance/time

=1130.9733/8

speed=141.37 ft/min.

Hence, the linear speed of the Ferris wheel is 141.37 ft/min.

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Answer:

Nathan will make $20

Jackson will make $29

hope you like it

The length Thebe the HCF (highest common factor) of the given dimensions that are 168mm and 196 mm. Hence, the length of each square will be equal to 28mm.

The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers. As a result, it is also known as the greatest common factor (GCF). If M is the greatest common factor of N, then M is the greatest possible number that divides N.

The length of the each square will be given by the HCF of the dimensions that are 168mm and 196mm.

[tex]168=2*2*2*3*7\\196=2*2*7*7[/tex]

So, the length of the each square paper=[tex]2*2*7=28mm.[/tex]

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The correct proportion to represent the triangle ABC is similar to triangle PQR is,

⇒ 4 / 9 = 12 / n

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

We have to given that;

Triangle ABC is similar to triangle PQR.

Hence, Corresponding sides of both triangles are equal to each other.

So, We ca formulate;

⇒ Base / Hypotenuse

⇒ 4 / 9 = 12 / n

Thus, Correct proportion to represent the triangle ABC is similar to triangle PQR is,

⇒ 4 / 9 = 12 / n

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The rate of change between Thursday and Friday is 6 minutes per day.

How to convert Hours to Minutes?

As we know 1 hour = 60 minutes. Here we can see that 60 minutes come together to form an hour hence we can conclude that hour is a bigger unit . Whenever we convert a bigger unit to a smaller unit we always multiply the bigger unit with the smaller unit from relation.

1 hr.= 60 min.

Minute is smaller so we will multiply by 60.

5 hr.= 5×60= 300 min.

10 hr.= 10×60= 600 min.

As we know 1 hour = 60 minutes. Here we can see hour is a bigger unit than minutes ones. Whenever we convert a smaller unit to the bigger unit we always divide the bigger unit number with the smaller unit number of the relation.

1 hr.= 60 min

here minute is smaller so we will divide out question by 60.

240 min = [tex]\frac{240}{60}[/tex] = 4 hr.

360 min = [tex]\frac{360}{60}[/tex] = 6 hr.

Now for the given question:

Time taken by Jackson to complete homework on Thursday= 35 min.

Time taken by Jackson to complete homework on Friday= 41 min.

Rate of change = (Time taken by Jackson to complete homework on Friday)-(Time taken by Jackson to complete homework on Thursday)

        = 41 - 35

        = 6

Note: for rate of change we always subtract smaller number from the bigger one.

Hence rate of change of time taken by Jackson to complete its homework between Thursday and Friday is 6 minutes per day.

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we assign the 8 teachers in 4 schools if each school is to receive at least one teacher and n more than 3 in  (8/4)⋅4!⋅4^4

Total teachers =8

Total schools =4

Let 4 teachers go to each one of school=8/4.4!

Distribute the other 4 teachers to the 4 schools: 4^4

Total: (8/4)⋅4!⋅4^4

In this question be used probability .permutation and combination.

Probability  is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind probability. For example, if a coin is tossed, the theoretical probability of getting a head will be ½.

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order. For example, the permutation of set A={1,6} is 2, such as {1,6}, {6,1}. As you can see, there are no other ways to arrange the elements of set A.

In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

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Answer:

Step-by-step explanation:

You want to solve the triangle with A=35°, B=60°, and c=10.

When two angles and a side are given, the Law of Sines is useful for providing a solution. In order to use it, we need to know an angle and its opposite side. That is, we need angle C.

Using the sum of angles of a triangle, we have ...

  A +B +C = 180°

  C = 180° -A -B = 180° -35° -60° = 85°

Now, we can use ...

  a/sin(A) = b/sin(B) = c/sin(C)

  b = c·sin(B)/sin(C) = 10·sin(60°)/sin(85°) ≈ 8.69

  a = c·sin(A)/sin(C) = 10·sin(35°)/sin(85°) ≈ 5.76

The distance travelled was 225 miles.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Average speed = 50 miles per hour

Time taken = 4 1/2 hours = 4.5 hours

Speed can be calculated using the formula,

Speed = Distance / Time

Distance = Speed × Time

               = 50 × 4.5

               = 225 miles

Detroit was 225 miles away.

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Yes, the average family size obtained from asking students at an elementary school would likely be biased. The average is likely to underestimate the true value of the family size for the population.

This is because a student’s family size only includes individuals who are living in the same household as the student and not everyone in the family.

For example, the student's siblings who have left the household to attend college or have moved out for other reasons would not be included in the student's family size estimate. Additionally, grandparents, uncles, aunts, and cousins who may also be part of the family are not included. Thus, the average family size obtained from asking students would be lower than the true average family size for the population.

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Answer:

She has less than $7

Step-by-step explanation:

$14.50 - $3.99 - $5.29 = $5.22

She has less than $7 because 7 is greater than 5.22.

$7>$5.22

The correlation coefficient is 0, implying that there is no linear relationship between the two variables.

The correlation coefficient is a measure of how strongly two variables are linearly related. The value of the correlation coefficient is between -1 and +1. A correlation coefficient of zero (0) implies that there is no linear relationship between the two variables. This means that the variables do not change in relation to each other; that is, if one variable goes up, the other variable does not necessarily go up or down.

The formula of correlation coefficient is given by:

r = ∑(x - X)(y - Y)/√[∑(x - X)2∑(y - Y)2]

where,

r = correlation coefficient

x = independent variable

X = mean of independent variable

y = dependent variable

Y = mean of dependent variable

When the correlation coefficient (r) is 0, this means that the two variables have no linear relationship. This can be calculated by substituting the values of x,X, y, and Y in the formula for the correlation coefficient.

For example, if x = 4, X = 3, y = 5 and Y = 4, then the correlation coefficient (r) can be calculated as follows:

[tex]r = [4 - 3)(5 - 4)]/√[(4 - 3)2 (5 - 4)2] r = (1)(1)/√[12] r = 1/√12 r = 1/3.464[/tex]

Thus, the correlation coefficient is 0, implying that there is no linear relationship between the two variables.

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Answer:

Below

Step-by-step explanation:

Circumference = pi * d = 22/7 * d

2517 = 22/7 * d             ( are you sure 2517 is correct??)

d = 2517 * 7/22 = 800.86 inches    ( a VERY large pie)

radius = 1/2 * d = 400.43 inches

Area = pi r^2

        = 22/7   * (400.43)^2 = 503 943 in^2

The correct answer is Stratified Random Sampling

Given that,

In a study, the sample is selected by dividing the class into gender-based groups, then choosing 10 men and 10 women.

Researchers split a population into homogeneous subpopulations called strata (plural of stratum) depending on particular traits in a stratified sample (e.g., race, gender identity, location, etc.).

In order to estimate statistical measures for each subpopulation, each stratum is then sampled using a different probability sampling technique, such as cluster sampling or simple random sampling.

When a population's traits are varied and researchers want to make sure that each characteristic is accurately represented in the sample, they rely on stratified sampling. This aids in the study's validity and generalizability while preventing biases in the research process like undercoverage bias.

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Answer:

x=-2.083

or x=-25/12

Step-by-step explanation:

Answer:

x = -25/12

Step-by-step explanation:

We can solve for x by isolating x:

[tex]((-12x-7)=18)+7\\((-12x=25)/12\\x=-25/12[/tex]

The measurement of acute triangle ABC we can find by direct substitution of the labeled measures in the Law of Sines is,

a/ sin a = b/sin b

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sine rule for a triangle ABC is, a/sinA = b/sinB = c/sinC .

In the diagram, there are two identified sides and if you use the sine rule, you can find the opposed angles easily.

Side a, with angle A.

Side b, with angle B.

If you input these into the sine rule, it would be, a/ sin a = b/sin b

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The compound inequality would be: 0 <= x <= 5 or x >= 10

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

no more than 5 totts or more than 10 totts

Represent the variable with s

So, we have the following representation

x no more than 5 totts or x more than 10 totts

As an inequality, we have

0 <= x <= 5 or x >= 10

See attachment for the graph

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The two forms of representing her hair length are (3/4)H cm and 0.75H cm.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, On Monday, Florencia's hair was H centimeters long.

Therefore, After the hair cut her hair length will be,

= (75/100)×H.

= (3/4)H cm.

Now, We can also write it in terms of decimals which is,

= (75/100)×H.

= 0.75H cm.

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For a standard normal distribution (mean = 0, standard deviation = 1), 80% of the data falls below a z-score of approximately 0.84.

A z-score represents the number of standard deviations a data point is from the mean of the standard normal distribution. For example, if a data point has a z-score of 1.96, it is 1.96 standard deviations above the mean of the standard normal distribution.

Standard normal distribution tables give the area under the standard normal curve to the left of a given z-score. The area to the right of a z-score is simply 1 minus the area to the left of the z-score. So if we want to find the z-score that corresponds to 80% of the data above it, we would look for the z-score that has an area of 0.2 to its right. The closest value listed on a standard normal distribution table to 0.84 is typically 0.841, which corresponds to an area of 0.2 under the standard normal curve to the right of that z-score.

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(a) The markup is $3.9.

(b) The selling price of the CD is $11.70.

The markup of the CD is calculated by applying the following formula.

The markup = 50% x $7.80

The markup = ( 50 / 100 ) x $7.80

The markup = 0.5 x $7.80

The markup = $3.9

The selling price of the CD is calculated as follows;

selling price = $7.80 + $3.9

selling price = $11.7

Thus, the selling price of the CD is a function of the cost price, and mark up price. So the final selling price of the CD is $11.7 while the mark up is $3.9

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The probability of exactly one processor having no jobs is 4/9 when a  computing center has 3 processors that receive n jobs.

The probability that exactly one processor has no jobs can be calculated using the binomial distribution. The number of successful trials (having exactly one processor with no jobs) is denoted by k and the total number of trials (number of ways to assign n jobs to 3 processors) is denoted by n. The probability of success in each trial is 1/3 (the chance that a particular processor has no jobs) and the probability of failure is 2/3 (the chance that a particular processor has one or more jobs).

Using the formula for binomial distribution, the probability that exactly one processor has no jobs can be calculated as follows:

[tex]P(X = k) = (n choose k) * (1/3)^k * (2/3)^{(n-k)}[/tex]

where (n choose k) is the number of combinations of n items taken k at a time, and can be calculated as n! / (k! * (n-k)!).

For the given scenario, n = 3 and k = 1, so the probability of exactly one processor having no jobs is:

[tex]P(X = 1) = (3 choose 1) * (1/3) * (2/3)^2 = 3 * (1/3) * (4/9) = 4/9.[/tex]

Hence, the probability of exactly one processor having no jobs is 4/9.

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Jesse engage in self injuries behavior every time he is denied access to the ipad and when it occurs we tally one mark on the data sheet it represents the Frequency

The frequency (f) of a specific fee is the variety of times the value takes place in the facts. The distribution of a variable is the pattern of frequencies, that means the set of all viable values and the frequencies associated with those values. Frequency distributions are portrayed as frequency tables or charts.

As a statistical device, a frequency distribution affords a visible illustration of the distribution of observations within a particular check. Analysts often use a frequency distribution to visualise or illustrate the facts accrued in a pattern

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1) Sales tax is a levy imposed on consumption by the government.

2) If you buy a meal from a restaurant that costs $15.00, and the tax is 7%, the sales tax is $1.05.

A sales tax is a consumption tax imposed by the government, state or local, on certain categories of goods.

The purpose of imposing a sales tax is to regulate the consumption of certain goods and improve the taxation revenue of the government.

The cost of a restaurant meal = $15.00

Sales tax rate = 7%

Sales tax in dollars = $1.05 ($15 x 7%)

Thus, for purchasing a meal that costs $15.00, the amount paid for taxes is $1.05, if the sales tax is 7%.

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The graph of the inequality -3x + y ≥ 1 is given below.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality:

-3x + y ≥ 1.

The intercepts are (0, 1) and (-0.33, 0)

The graph of the inequality is given in the attached image.

Therefore, the graph is given.

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Using the graph we will see that line q can be written as:

y = (-1/2)*x + 3

Remember that the general linear equation is written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Using the graph we can identify the two points (0, 3) and (2, 2), then the slope is:

a = (2 - 3)/(2 - 0) = -1/2

And the y-intercept is y = 3, then the linear equation is:

y = (-1/2)*x + 3

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