what are the different methods in finding the LCM​

The smallest perimeter and dimensions of rectangle having area of 169 [tex]inches^{2}[/tex] is 52 inches , length 16 inches and breadth also 16 inches.

Given that the area of rectangle is 169 [tex]inches^{2}[/tex].

We have to find the smallest perimeter and dimensions of the rectangle.

let the length of rectangle be x inches and breadth be y  inches.

We know that area of rectangle is the product of its length and breadth. So,

Area=xy

169=xy

y=169/x

Perimeter of rectangle =2(x+y)

Put the value of y=169/x in the perimeter.

P=2(x+169/x)

P=2x+338/x

Differentiate both sides with respect to x.

dP/dx=2-338/[tex]x^{2}[/tex]

Again differentiate it with respect to x.

[tex]d^{2} P/dP^{2}[/tex]=676/[tex]x^{3}[/tex]

Because the second derivative is greater than 0 so the perimeter is minimum.

Put dP/dx=0 to get the value of x.

dP/dx=0

2-338/[tex]x^{2}[/tex]=0

2=338/[tex]x^{2}[/tex]

[tex]x^{2}[/tex]=169

x=[tex]\sqrt{169}[/tex]

x=13

Put the value of x in y=169/x

y=169/13

=13

To calculate the perimeter, put the values of x and y in P=2(x+y)

P=2(13+13)

=2*26

=52 inches.

Hence The smallest perimeter and dimensions of rectangle having area of 169 [tex]inches^{2}[/tex] is 52 inches , length 16 inches and breadth also 16 inches.

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Answer:

I don't understand the array of numbers as written in the question.

Step-by-step explanation:

See attached image

The explanation about the graph is illustrated below.

The graph shows 0 to 30 on the x-axis at increments of 5 and 0 to 12 on the y-axis at increments of 1. The label on the x-axis is Temperature in degrees C, and the label on the y axis is the Number of Sweaters Sold.

If you will draw lines through, (12.5,6) and (15,4), it will best represent a line of best fit, because most of the points on the same and opposite sides of line are equidistant from each other.

Equation of line passing through (12.5,6) and (15,4) A line of best is the line that passes through all or some points or only through a single point, which describes the relationship between x and y values of data set

4x + 5y = 80

5y = -4x + 80.

y = -4x/5 + 16

Slope = -4/5 and y intercept is 16.

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The margin of error of this poll is

Given that 230 people were asked if they liked dogs, and 90% said they did.

In a random sample, a margin of error is a statistical measure that takes into account the discrepancy between actual and expected results.

Sample size (N)=230

Sample proportion  [tex](\hat{p})[/tex] = 90% = 0.90  and

confidence interval = 99%

The critical value at 99% confidence interval with α=0.01 is

[tex]\begin{aligned}Z_{c}&=Z_{1-\frac{\alpha}{2}}\\ &=Z_{1-\frac{0.01}{2}}\\ &=Z_{0.995}\\ &=2.576\end[/tex]

This value is taken from the Standard normal distribution table.

Now, we will calculate the margin of error (E) by using the formula

[tex]E=Z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{N}}[/tex]

Substituting the values in the formula, we get

[tex]\begin{aligned}E &=2.576\times \sqrt{\frac{0.90(1-0.90)}{230}}\\ &=2.576\times \sqrt{\frac{0.09}{230}}\\ &=2.576\times\sqrt{0.00039}\\ &=2.576\times 0.0197\\ &=0.0507\end[/tex]

Hence, the margin of error when 230 people were asked if they liked dogs, and 90% said they did is 0.0507.

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The correct answer is none of the above.

A line is defined as the shortest distance between two points and the point  where two lines meet is known as an angle.

From the given figure, the measure of angle a and b are supplementary since the sum of the angles is not 180 degrees.

They are not vertical angles since they do not meet at a point of intersection

The measure of angle a and b are complementary since the sum of the angles is not 90 degrees. Hence the correct answer is none of the above.

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The diagonal of the rectangle solid is [tex]\sqrt{50[/tex]

The dimensions are given as:

3,4,5

The diagonal is calculated as:

[tex]d = \sqrt{3^2 + 4^2 + 5^2[/tex]

This gives

[tex]d = \sqrt{50[/tex]

Hence, the diagonal of the rectangle solid is [tex]\sqrt{50[/tex]

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The probability computed shows that there ia enough evidence to support the director's claim.

From the information given, the hospital director is told that 79% of the emergency room visitors are insured.

p = 0.79

q = 1 - 0.79 = 0.21

The computation of the z value is -1.91. This is a two tailed test.

The p-value will be:

= P(Z < -1.91)

= 0.0562 under the distribution table.

In this case, the p value is less than 0.10, therefore, we reject the null hypothesis.

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Answer:

900

Step-by-step explanation:

Answer:

31.

Step-by-step explanation:

We have the equation:

(2x - 17) / 3 = 15     where x is the number to be found.

Multiply both sides by 3:

2x - 17 = 45

2x = 45 + 17 = 62

x = 31.

The number of weeks it will take for the budget money to run out is; 2 weeks.

The number of weeks it would take for the budget money to decrease till it runs out as required in the task can be interpreted as the x-value which corresponds to a Y-value of zero.

Hence, by setting y=0; we have;

-2x -0 = -4

-2x = -4

Divide both sides of the equation by; -2.

x = 2

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Using the Fundamental Counting Theorem, there are 15 ways to travel from Andy's house to Willie's house.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, the parameters are:

[tex]n_1 = 3, n_2 = 5[/tex].

Hence the number of ways is:

N = 3 x 5 = 15.

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Answer:

[tex]\frac{5x+2}{(x-4)(x+7)}[/tex]

Step-by-step explanation:

to obtain a common denominator

multiply the numerator/denominator of the first fraction by x + 7

multiply the numerator/denominator of the second fraction by x - 4

= [tex]\frac{2(x+7)}{(x-4)(x+7)}[/tex] + [tex]\frac{3(x-4)}{(x-4)(x+7)}[/tex]

simplify and add numerators leaving the common denominator

= [tex]\frac{2x+14+3x-12}{(x-4)(x+7)}[/tex]

= [tex]\frac{5x+2}{(x-4)(x+7)}[/tex]

Answer:

We have,

According to given figure.

PQ=PR(giventhat)

QS=SR(Bydefinationofmidpoint)

PS=PS(Commonline)

Then,

ΔSPQ≅ΔSPR   (BY congruency S.S.S.)

Hence, PS bisects ∠PQR by definition of angle bisector.

Question:

A sample of cans of peaches was taken from a warehouse, and the content of each can mearsed for weight. the sample means was 486g with stand deviation 6g. state the weight percentage of cans with weight:

Draw normal curve to help - split into 8 section ( i can't draw it here)

a) 34.13% of cans will be between 480g and 486g.

b) 13.59 + 2.15 + 0.13= 15.87% of cans greater than 492g.

Look at the Stand Dev Graph where the give you the number

Step-by-step explanation:

Let me give you a different question and i will answer it, which you help you answer your question.

The solution to the system of equations is one solution at (2, -2)

The system of equations is given as:

4x + 3y = 2

3x − 2y = 10

Multiply (1) by 2 and (2) by 3.

So, we have:

8x + 6y = 4

9x − 6y = 30

Add both equations

17x = 34

Divide by 17

x = 2

Substitute x = 2 in 3x − 2y = 10

3(2) − 2y = 10

Solve for y

y = -2

Hence, the solution to the system of equations is one solution at (2, -2)

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Depending on the number of teams, the possible numbers of students per team are in the set:

{2, 3, 4, 6, 9, 12, 18}

We know that there are 36 students divided equally into N teams.

Such that the number of teams is larger than 1 and smaller than 20.

Then we could have 2 teams, such that the number of students in each team is given by the quotient between the total number of students and the number of teams.

36/2 = 18

There are 18 students in each team.

Notice that the numbers of teams can only be factors of 36, where:

36 = 6*6 = 2*2*3*3

So the factors are:

2, 3, 2*3, 3*3, etc...

If there are 3 teams we have:

36/3 = 12 students per team.

If there are 6 teams we have:

36/6 = 6 students per team.

if there are 9 teams:

36/9 = 4 students per team.

If there are 12 teams:

36/12 = 3 students per team.

If there are 18 teams:

36/18 = 2 students per team.

These are all the possibilities.

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To predict the bagel sales numbers for the next month, Leigh could use Predict trend.

Given that Leigh has information on how many customers purchase bagel at her coffee shop.

We are required to answer the spreadsheet Leigh could use to predict bagel sales number for the next month.

Spreadsheet is developed for windows, macOS, Android and iOS.It features calculation through functions. In this we can use mathematical functions,logical functions, etc.

Leigh could use predict trend to predict the sales number of bagels of next month.

Hence predict trend could be used by Leigh to predict the sales for the next month.

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Question is incomplete as question should include the following:

What spreadsheet could Leigh use to predict the sales of next month?

The area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3

The curve is given as:

y = √(x + 3)

The area bounded by the curve, x-axis and y-axis is when x = 0 and y = 0

When y = 0, we have:

0 = √(x + 3)

This gives

x = -3

So, we set up the following integral

A = ∫ f(x) d(x) (Interval a to b)

This gives

A = ∫ √(x + 3) d(x) (Interval -3 to 0)

When the above is integrated, we have:

A = 1/3 * [2(x + 3)^(3/2)] (Interval -3 to 0)

Expand

A = 1/3 * [2(0 + 3)^3/2 - 2(-3 + 3)^3/2]

This gives

A = 1/3 * 2(3)^3/2

Apply the law of indices

A = 2(3)^1/2

Rewrite as:

A = 2√3 or 3.46

Hence, the area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3

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The expression for g in terms of other variables is g = Fd^2/m1m2

Given the expression below as shown

F=gm1*m2/d2

We are to make g the subject of the formula

F=gm1*m2/d2

Cross multiply

Fd2 = gm1m2

Divide both sides by m1m2

Fd^2/m1m2 = g

g = Fd^2/m1m2

Hence the expression for g in terms of other variables is g = Fd^2/m1m2

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Answer:

|-1| + |3|

Step-by-step explanation:

We can use absolute values to find the distance between positive and negative numbers on a number line.

|-1| + |3| =

Keep in mind that

- the absolute value of a positive number is positive and

- the absolute value of a negative number is positive

1 + 3 =

4 units

Answer: 4

Step-by-step explanation:

The points are (-1, 1) and (5, 5).

So, the difference in the y coordinates is [tex]5-1=4[/tex].

The net change between the x-coordinates and y-coordinates on the graph is 6 units and 4 units respectively.

The coordinates from the given graph are (5, 5) and (-1, 1).

Given two points, (a, f(a)) and (b, f(b)) on the graph of f(x), the net change is the difference between the two f(x) values. Thus, net change is given by f(b)−f(a).

Here, the change in x-coordinates is 5-(-1) = 6

The change in y-coordinates is 5-1 = 4

Therefore, the net change between the x-coordinates and y-coordinates on the graph is 6 units and 4 units respectively.

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Solving the given equation, the value of v that makes the statement true is:

A. v = 8.

The equation is:

[tex]12 = 12 + \frac{v - 8}{2}[/tex]

Hence:

[tex]\frac{v - 8}{2} = 0[/tex]

Applying cross multiplication:

v - 8 = 0

v = 8.

Hence option A is correct.

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Answer:

Step-by-step explanation:

We are given two sides and one angle opposite to one of the known sides.

In order to find the missing side we need to use the law of sines.

Find the angle opposite to the second known side, let it be x.

Find the missing third angle y, using angle sum theorem:

Find the required side length z, the distance from the plane to the observer tower, using the law of sines again.

Note. At this point you can use the law of cosines as we have found the angle between the known sides.

So the required distance is 7.7 km

It is a good practice for a server or bartender to not take patrons' drink orders too quickly

A bartender a person who prepares or serves alcoholic and some non-alcoholic beverages from behind a bar.

Below are some of the duties or responsibilities of a bartender:

So therefore, it is a good practice for a server or bartender to not take patrons' drink orders too quickly

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Answer:

math math math math math math math math math math

The term used to describe a customer who sees a pair of boots online but then decides to buy the same pair at Macy's after trying them on would be best classified as a cross-channel shopper.

A cross-channel shopper is a consumer who uses various combination of both several channels for the same purchase.

The customer has checked the pair of boots online but rather purchased the same boots at Macy's instead of purchasing online.

Therefore, a cross-channel shopper uses different purchasing channel to purchase a product.

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At office 826 they will meet if they leave at the same time.

It is given that,

Agent J has recently been relocated from office 2013 to office 1. But his former office neighbor, Agent K is still in office 2014.

So, there are  (2014 - 1) - 1 = 2012 offices in between them.

It is given that,

Agent J can walk at a rate of 25 offices per minute, and Agent K walks at 36 offices per minute.

So,

Per minute they cross

= 25 + 36

= 61 offices.  

Thus, the time required for crossing all the 2012 offices is,

= 2012/61

= 32.9 ≅ 33 minutes

Then,

They will meet at

1 + 25(33) = 826 office (or)

2014 - 36(33) = 826 office (Negative since opposite direction)

Therefore, both of them meet at office 826.

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Answer:

b

Step-by-step explanation:

using the recursive rule [tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] - 1 and a₁ = 2 , then

a₂ = 3a₁ - 1 = (3 × 2) - 1 = 6 - 1 = 5

a₃ = 3a₂ - 1 = (3 × 5) - 1 = 15 - 1 = 14

a₄ = 3a₃ - 1 = (3 × 14) - 1 = 42 - 1 = 41

a₅ = 3a₄ - 1 = (3 × 41) - 1 = 123 - 1 = 122

The solution to the equation (x+21)=7 is x = -14

The equation is given as:

(x+21)=7

Remove the brackets

x + 21 = 7

Subtract 21 from both sides

x + 21 - 21 = 7 - 21

Evaluate the expression

x = -14

Hence, the solution to the equation (x+21)=7 is x = -14

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The conversion factor of the chicken recipe used at the banquet is 4.5.

An equation is an expression that shows the relationship between two or more variables and numbers.

Conversion factor = (new amount * portion size) / (old amount * portion size)

Hence:

Conversion factor = (60 * 3) / (10 * 4) = 4.5

The conversion factor of the chicken recipe used at the banquet is 4.5.

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