In estimating √60, the two perfect squares that provide the best two benchmarks to estimate
the answer can be represented by the numbers _____ and_______.
Write the smallest
perfect square in the first two boxes and the largest perfect square in the last two boxes.

Answers

Answer 1

Answer:

60 falls between two perfect squares: 49 (72), and 64 (82).

Step-by-step explanation:


Related Questions

in a test of the difference of two proportions, the z-value was calculated to be 1.69. compute an upper tail, lower tail, and two tail p-values for this test statistic.

Answers

By using the z value, it can be calculated that

P value for upper tail = 0.0455

P value for lower tail = 0.9545

P value for two tail  = 0.091

What is z value?

z value determines the number of standard deviation, the event is above the mean value. That means z value determines the distance of the event from the mean and it is measured in terms of Standard Deviation.

z value = 1.76

From the z table

P value for upper tail = 1 - 0.9545 = 0.0455

P value for lower tail = 0.9545

P value for two tail = 0.0455 [tex]\times[/tex] 2 = 0.091

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as a seismologist, janet understands the devastating effects that earthquakes can have. so, she keeps her basement stocked with canned food, like chili. janet buys cans of chili from an online retailer that charges a shipping fee plus the cost of each can of chili. this table shows the relationship between the number of cans of chili janet buys, x, and the total cost (in dollars), y. x (cans) y (dollars) 12 $26.40 44 $56.80 66 $77.70 100 $110 according to the values in the table, do x and y have a proportional relationship?

Answers

As a seismologist, Janet understands the devastating effects that earthquakes can have. so, she keeps her basement stocked with canned food, like chili. This table shows the relationship between the number of cans of chili Janet buys, x, and the total cost (in dollars), y.

[tex]\begin{tabular}{|c|c|c|}\underline{x(cans)}&\underline{y(dollars)} \\12 & \$\ 26.40 \\ 44 & \$\ 56.80 \\ 66 & \$\ 77.70 \\ 100 & \$\ 110 \end{align}[/tex]

According to the values in the table, x and y have not a proportional relationship.

Prove x and y have a proportional relationship

Table

[tex]\begin{tabular}{|c|c|c|}\underline{x(cans)}&\underline{y(dollars)} \\12 & \$\ 26.40 \\ 44 & \$\ 56.80 \\ 66 & \$\ 77.70 \\ 100 & \$\ 110 \end{align}[/tex]

Specifies the gradient (m) in rows 1 and 2

m₁ = [tex]\displaystyle \frac{56.80 - 26.40}{44-12}[/tex]

m₁ = [tex]\displaystyle \frac{30.40}{32}[/tex]

m₁ = [tex]\displaystyle \frac{19}{20}[/tex]

Specifies the gradient (m) in rows 2 and 3

m₂ = [tex]\displaystyle \frac{77.70 - 56.80}{66-44}[/tex]

m₂ = [tex]\displaystyle \frac{20.9}{22}[/tex]

Because the values of m₁ and m₂ are not the same [tex]\displaystyle \frac{19}{20}[/tex] ≠ [tex]\displaystyle \frac{20.9}{22}[/tex], then x and y have not a proportional relationship.

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How do you determine which table represents a function?.

Answers

We can determine which table represents a function by, verifying each input value's pairing with a single output value.

Define function.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given,

We can determine which table represents a function by,

Determine whether a table of input and output values constitutes a function. Determine the values for the input and output. Verify each input value's pairing with a single output value. In that case, the table is a function.

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Lacy ha 10 gallon of water. She pour an equal number of gallon of water into each of 3 fih tank. Lacy' blue fih tank already ha 1 third gallon of water in it. How many gallon of water doe lacy blue fih tank ha now? fi

Answers

Lacy's blue fish tank has now 3 2/3 gallons of water.

If Lacy has 10 gallons of water and she pour an equal number of gallons of water into each of her 3 fish tanks, then the amount of water each tank will have is equal to the quotient of 10 divided by 3.

amount of water poured in each tank =  10 gallons / 3

amount of water poured in each tank = 10/3 gallons

If Lacy's blue fish tank already has 1/3 gallon of water in it, then the total amount of water the blue fish tank has is the sum of the two fractions.

Add the initial amount and the amount poured in after.

1/3 + 10/3 = 11/3 =  3 2/3 gallons

Simplifying the fraction, Lacy's blue fish tank has now 3 2/3 gallons of water.

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What is an equation of the line that passes through the point ( 8 , 2 ) (8,2) and is parallel to the line x + 4 y = 28 x+4y=28?.

Answers

The equation of the line that passes through the point (8,2) and is parallel to the line x+4y = 28 is y = -x/4+4.

According to the question,

We have the following information;

Point thorough which line is passing = (8,2)

Equation of the line:

x+4y = 28

Now, we will convert this equation into the slope-intercept form:

4y = -x+28

Dividing by 4 on both sides of the equation:

y = -x/4+28/4

y = -x/4+7

Slope of the line = -1/4

We know that the following formula is used to find the equation of the line:

(y-y') = m(x-x')

(y-2) = -1/4(x-8)

y-2 = -x/4+2

Adding 2 on both sides:

y = -x/4+4

Hence, the equation of the line that passes through the point (8,2) and is parallel to the line x+4y = 28 is y = -x/4+4.

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rapheal pays 7$ for 1/2 pound of cashews how much would he pay for one pound

Answers

Answer:

$14

Step-by-step explanation:

since there are 2 halves in a pound we just need to multiply 7 by 2

7x2

14

Hopes this helps please mark brainliest

It's $7 for 1/2 a pound so we have to double it to get our answer so...

$14 would be our answer.

[tex]1/2+1/2=1[/tex]

What is -4 2/5÷(-5). I will give Big Brain.​

Answers

Brackets go first, then you have to do the multiplication and division, then addition and subtraction:

-42/5÷(-5) = (-42/5)÷(-5) = -42/(5 x -5) = -42/(-25) = 42/25

jessica and robert have two young children. they have $7,000 of qualified child care expenses and agi of $22,000 in 2021

Answers

The allowable child and dependent care credit considering their pre-credit tax liability is $0

The following chart illustrates how their authorized child and dependent care credit was calculated:

If the revenue is less than $22,000, the full 22% would be permitted.

However, the eligible kid expense would only be allowed up to $7,000.

Consequently, the sum would be

= $7,000 × 22%

= $1,540

Since there is already a pre-credit tax liability, $0 should be taken into account because there would be no credit.

Due to their pre-credit tax liability, the available child and dependent care credit is therefore $0.

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What is an outlier answer?.

Answers

If the data collection contains the following numbers: 3, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 85 , Here 3 and 85 represents the outlier.

What is characteristics of statistics ?

The important characteristics of Statistics are given as follows:

Statistics are always numerically expressed.It had an aggregate of facts and dataData are to be collected in systematic wayIt should be always comparable to each otherData are collected for a pre planned purpose

Outliers are the data's most wildly divergent values.

For instance, if the data collection contains the following numbers: 3 19, 25, 32, 36, 38, 31, 42, 57, 45, and 85

The display of data and outliers

The numbers 3 and 85, which are at the extremes and are hence outliers in the number line above, may be seen to be at these extremes.

The group's outliers are a part of it, but they are not close to the other group members.

Outliers are a concern since they cause an imbalance in the data set, which is why they are typically eliminated. Furthermore, an error can sometimes cause an outlier to appear in a data collection.

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Suppoe the domain of the propoitional functionP (x, y) conit of pair x and y, where x i 1, 2, or 3 and y i 1, 2, or 3. Write out thee propoition uing dijunction and conjunction. A) ∀x∀yP (x, y) b) ∃x∃yP (x, y) c) ∃x∀yP (x, y) d) ∀y∃xP (x, y)

Answers

These are the preposition for the given conditions:

(P(1,1) ∧ P(1,2) ∧ P(1,3)) ∧ (P(2,1) ∧ P(2,2) ∧ P(2,3)) ∧ (P(3,1) ∧ P(3,2) ∧ P(3,3)).

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∨ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∨ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∧ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∧ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

(P(1,1) ∧ P(1,2) ∧ P(1,3)) v (P(2,1) ∧ P(2,2) ∧ P(2,3)) v (P(3,1) ∧ P(3,2) ∧ P(3,3)).

The domain of the propositional P(x, y) consists of pairs x and y, where x is 1, 2, 3 and y is 1, 2, 3.

What are the disjunction and conjunction?

In logic functions, there are two kinds of compound statements. These are referred to as conjunction and disjunction. A conjunction implies that both statements are correct, whereas a disjunction implies that at least one of the statements is correct. A conjunction connects statements with the word "and," whereas a disjunction connects statements with the word "or."

By using disjunction and conjunction we get,

a) ∀x∀y P(x, y) is written as:

(P(1,1) ∧ P(1,2) ∧ P(1,3)) ∧ (P(2,1) ∧ P(2,2) ∧ P(2,3)) ∧ (P(3,1) ∧ P(3,2) ∧ P(3,3)).

b) ∃x ∃y P (x, y) is written as:

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∨ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∨ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

c) ∃x∀y P(x, y)  is written as:

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∧ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∧ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

d) ∀y∃x P(x, y)  is written as:

(P(1,1) ∧ P(1,2) ∧ P(1,3)) v (P(2,1) ∧ P(2,2) ∧ P(2,3)) v (P(3,1) ∧ P(3,2) ∧ P(3,3)).

Hence, these are the preposition for the given conditions:

(P(1,1) ∧ P(1,2) ∧ P(1,3)) ∧ (P(2,1) ∧ P(2,2) ∧ P(2,3)) ∧ (P(3,1) ∧ P(3,2) ∧ P(3,3)).

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∨ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∨ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

(P(1,1) ∨ P(1,2) ∨ P(1,3)) ∧ (P(2,1) ∨ P(2,2) ∨ P(2,3)) ∧ (P(3,1) ∨ P(3,2) ∨ P(3,3)).

(P(1,1) ∧ P(1,2) ∧ P(1,3)) v (P(2,1) ∧ P(2,2) ∧ P(2,3)) v (P(3,1) ∧ P(3,2) ∧ P(3,3)).

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Find the equation of a line perpendicular to y=x+1 that passes through the point (−2,8).

Answers

Answer:

y=-x+6

Step-by-step explanation:

For linear graphs, the slope of perpendicular lines must be of equal value but opposite in sign: ([tex]m_1=-m_2[/tex]).

The slope of y=x+1 is 1, therefore the slope of the perpendicular line must be -1.

Given (x,y)=(-2,8) the equation of the perpendicular line can be obtained by substituting these values into the slope-intercept form y=mx+b.

8=(-1)(-2)+b

8=2+b

6=b

So, the perpendicular line has a slope-intercept form of y=-x+6 or y=6-x.

Solve the following:
A.
Quality Control: A company has four photocopy machines A, B, C and D. The probability that a given machine will break down on a particular day is
P(A) = 13⁄100
P(B) = 9⁄50
P(C) = 1⁄5
P(D) = 13⁄100
Assuming independence, what is the probability on a particular day that all machines will break down?
a) 0.00164366
b) 0.00060840
c) 0.01000000
d) 0.00000234
e) 0.16436555
f) None of the above.

Answers

The probability on a particular day that all machines will break down is 0.00060840. So the option b is correct.

In the given question,

A company has four photocopy machines A, B, C and D.

The probability that a given machine will break down on a particular day is;

P(A) = 13⁄100

P(B) = 9⁄50

P(C) = 1⁄5

P(D) = 13⁄100

We have to find the probability on a particular day that all machines will break down.

The required probability = P(A∩B∩C∩D)

The required probability = P(A)∙P(B)∙P(C)∙P(D)

The required probability = 13⁄100 × 9⁄50 × 1⁄5 × 13⁄100

The required probability = 1521/2500000

The required probability = 0.00060840

Hence, the probability on a particular day that all machines will break down is 0.00060840. So the option b is correct.

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consider the set of integers from 1 to 20 inclusive. this set has how many 3-element subsets, such that no two consecutive integers are in the subset?

Answers

It has 816 ways to 3-element subsets, such that no two consecutive integers are in the subset.

You need three digits from 1 to 20, but you don't want any consecutive ones. You should call them a, b, and c.

Without loss of generality, a < b < c.

We use combinations,

Remember that we can write a + 1 b if a b and they're not sequential. With the aid of this insight, we can see the number of desired the number of methods for choosing a, b, and c from among the integers so that,

(1 ≤ a) & (a + 1 < b) & (b + 1 < c) & (c ≤ 20)

In other words, you want to know how many possibilities there are to choose the three numbers a, b, and c so that;

1 ≤ a < b − 1 < c − 2 ≤ 18

As a result, the question is equal to asking how many ways there are to select three integers (a, b - 1, and c - 2) from a range of 1 to 18. In other words, we are interested in how many ways we can select three items from a total of 18 options.

So, the response is:

[tex](^1^8_3)[/tex] = 816 ways

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if the pile contains only 15 quarters and only 20 dimes but at least 30 of each other kind of coin, how many collections of 30 coins can be chosen?

Answers

The number of ways to choosing coins with at least 15 quarters and 20 dimes is 4354.

In the given question, if the pile contains only 15 quarters and only 20 dimes but at least 30 of each other kind of coin, then we have to find the collections of 30 coins can be chosen.

Number of coins only of quarters = 15

Number of coins only of dimes = 20

The number of ways to choosing coins with at least 15 quarters and 20 dimes= Total- [tex](^{18}C_{3}+^{13}C_{3})[/tex]

The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]^{33}C_{3}-(^{18}C_{3}+^{13}C_{3})[/tex]

Using [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]

The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]\frac{33!}{3!(33-3)!}-(\frac{18!}{3!(18-3)!}+\frac{13!}{3!(13-3)!})[/tex]

The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]\frac{33!}{3!30!}-(\frac{18!}{3!15!}+\frac{13!}{3!10!})[/tex]

Simplifying

The number of ways to choosing coins with at least 15 quarters and 20 dimes= [tex]\frac{33\times32\times31\times30!}{3\times2\times1\times30!}-(\frac{18\times17\times16\times15!}{3\times2\times1\times15!}+\frac{13\times12\times11\times10!}{3\times2\times1\times10!})[/tex]

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 11×16×31-(3×17×16+13×2×11)

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 5456-(816+286)

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 5456-1102

The number of ways to choosing coins with at least 15 quarters and 20 dimes= 4354

If the pile contains only 15 quarters and only 20 dimes but at least 30 of each other kind of coin, the number of ways to choosing coins with at least 15 quarters and 20 dimes is 4354.

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The line egment i rotated 270 degree clockwie about the origin to form P'Q'. Which tatement decribe P'Q'

Answers

The line segment i rotated 270 degree clockwise about the origin to form P'Q' the statement describe P'Q'. The accurate alternative is (B) P'Q' is same in period to PQ.

That line phase PQ is proven at the co-ordinate grid. The line phase PQ is turned around 270 ranges counter clockwise approximately the foundation to shape P'Q'.We are to pick out the announcement that describes P'Q'.From the graph, we observe that the co-ordinates of factor P are(- 5, 3) and the co-ordinates of Q are (- 1, 3) .So, the period of PQ as calculated the usage of distance system is given byPQ = [tex]sqrt((- 1 + 5) + (- 3 + 3) ) = sqrt(+ )[/tex] = 4 units.We understand that if a factor is turned around 270 ranges counterclockwise, then its co-ordinates modifications as follows:(x, y) -> (y, - x)So, after the rotation, the co- ordinates of P and Q becomes[tex]P(-5,3) P^ (3, 5)G(- 1, 3) Q^ (3,1[/tex].The period of the road phase P'Q' as calculated the usage of distance system isP^ top Q^ top = sqrt([tex](3 - + (1 - ) = sqrt[/tex]= 4 units.Thus, the lengths of PQ and P'Q' are same.

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What is an example of a linear function?.

Answers

2x+y-3 = 0 iS a linear function with coefficient as 2 and 1 with constant part c = 3.

What is linear function ?

In a graph, a linear function is one that generates a straight line. The degree of the polynomial function is often either maximum 1 or minimum 0. Despite the fact that both calculus and linear algebra can be used to express linear functions. The function notation is the only thing that differs. Also required is the ability to read an ordered pair expressed in function notation. A function is denoted by the notation f(a), where an is an independent variable on which the function depends. The straight line on the linear function graph contains the expression or formula;

Linear function can be always represented in the format of ax + by + c = 0.

Here,

a € ( -∞, +∞)

b € ( -∞, +∞)

c € ( -∞, +∞)

Hence, Linear expression always contains y¹ and x¹.

and can always be represented in the form of y = mx.

So it always represents the straight line.

For example: 2x+y-3 = 0 ia a linear expression with coefficient as 2 and 1 with constant part c = 3.

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What are the steps to solving a polynomial?.

Answers

If solving an equation, put it in standard form with 0 on one polynomial side and simplify.

How to solve it?

If you're down to a linear or quadratic equation (degree 1 or 2),

solve by inspection or the quadratic formula. Find one rational factor or root. Divide by your factor.

Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.

How do you solve a polynomial problem in four steps?

Put the equation in standard form with 0 on one side to simplify it while solving it.

Know the anticipated number of roots.

If you're left with a linear or quadratic equation of degree 1 or 2, use the quadratic formula or visual inspection to solve it.

Identify one logical cause or source.

Subtract from your factor.

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2.2(z + 3) − 1.93 = 6.87

Answers

Answer:

z=1

Step-by-step explanation:

2.2(z+3)-1.93=6.87

2.2z+6.6-1.93=6.87

2.2z+4.67=6.87

       -4.67. -4.67

2.2z=2.2

/2.2. /2.2

z=1

Hopes this helps please mark brainliest

Answer:

z = 1

Step-by-step explanation:

2.2(z + 3) − 1.93 = 6.87

1. Distribute

2.2z + 6.6 - 1.93 = 6.87

2. Combine Like Terms

2.2z + 4.67 = 6.87

3. Subtract 4.67 on both sides

2.2z + 4.67 = 6.87

        - 4.67  - 4.67

2.2z = 2.2

4. Divide both sides by 2.2

[tex]\frac{2.2z}{2.2} = \frac{2.2}{2.2}[/tex]

z = 1

Two boat AandB left a portC at the ame time on different route. B travelled on a bearing of 150 and A travelled on the north ide of B. When A had travelled 8km andB had travelled 10km ,the ditance between the two boat wa found to be 12km. Calculate the bearing ofA, route from C

Answers

The bearing of A route from C is  67.2°.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which means "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

Here, we have

B traveled on a bearing of 150 and A traveled on the north side of B.

To find angle C, we have to use the cosine rule and we get

12² = 8² + 10² - 2 × 8 × 10 × cosC

C = 82.8°

The bearing of A from C will be

= 150° - 82.8°

= 67.2°.

Hence, the bearing of the A route from C is  67.2°.

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a wheat farmer has a storage bin that holds 6,846 1/4 cubic feet.if a bushels of wheat fills 11/4 cubic feet, how many bushels cam the storage bin hold

Answers

The storage bin can hold 5477 bushels.

We have total capacity of the storage bin which is given to us in mixed fraction form.

If we convert this into improper fraction, it is equivalent to =27385/4

Now, in the same way ,we have also given that  some amount of wheat already fills which is also given in mixed fraction form.

If we convert this into improper fraction form, it is equivalent to

=5/4

Now, to find the the number of bushels storage bin maximally hold is =(total volume of storage bin)/(Volume of wheat fills)

=>N = (27385/4)/(5/4)

=>N=27385/5

=>N=5477

Hence, total number of bushels which storage bin can hold is 5477.

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given the cost information below, if this firm increases its production and sales from 3 to 4 units per day, given a market price of $2,500 per unit, the profit margin

Answers

If the firm increases its production and sales from 3 to 4 units per day, the profit margin increases.

The correct answer option is option B

What is the profit margin?

Total profit = Total revenue - Total cost

Total revenue = number of units × price of each Units

Market price of the commodity = $2,500

At 3 units:

Total profit = Total revenue - Total cost

= (3 × 2500) - $3000

= $7,500 - $3000

Total profit = $4,500

At 4 units:

Total profit = Total revenue - Total cost

= (4 × $2,500) - $4,100

= $10,000 - $4,100

= $5,900

In conclusion, the profit margin when production is increased from 3 to 4 units will also increase.

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Determine the equations of the elastic curve using the coordinates x1 and x2 and specify the deflection and slope at C. El is constant.

Answers

The equations of the electric curve using the coordinates x₁ and x₂ are:

For AB:

y₁= (1/EI) [-M₀x₁³/6L  + M₀ Lx₁/6]

For CB:

y₂= (1/EI) [-M₀x₂²/2   + 3M₀Lx₂/2  - M₀L]

What is meant by elastic curve?

The elastic curve of a beam is the curve formed by the intersection of the neutral surface and the side of the beam when the longitudinal stresses on the fibers.

An Elastic curve is flatter, resembling the horizontal lines in the letter E. Price elasticity of demand, also known as demand elasticity, relates to the degree of responsiveness in demand quantity with respect to price.

For AB:

[tex]M_{x}[/tex]= - [tex]A_{y}[/tex]x₁

By using double integration method,

EI y₁"=[tex]M_{x}[/tex]= - [tex]A_{y}[/tex]x₁

EI y₁'=- [tex]A_{y}[/tex](x₁)²/2   +C₁   -------(1)

EI y₁=- [tex]A_{y}[/tex](x³/6)+C₁ x +C₂   -------(2)

The boundary conditions are:

At x₁=0, y₁=0

At x₁=L, y₁=L

y₁=0,

=- [tex]A_{y}[/tex](0)+C₁ (0) +C₂

Then, C₂=0

y₁=L,

=- [tex]A_{y}[/tex](L³/6)+C₁ (L) +0

Then, C₁= [tex]A_{y}[/tex](L²/6)

C₁=M₀L/6

EIy₁'= -M₀L((x₁)²/2) ------(3)

EIy₁ = -M₀L((x₁)³/6)+(M₀L/6)x₁   -----(4)

For CB:

Mₓ= -M₀

x₂ is in opposite direction to x₁

So the integration with respect to x₂ will be alternately signed.

EI y₂"=Mₓ= -M₀

EI y₂'= -(-M₀x₂)+C₃

EI y₂'=M₀x₂+C₃ ------(5)

EI y₂= -M₀((x₂)²/2)-C₃x₂+C₄ ------(6)

The boundary conditions are:

x₂=L, y₂'=y₁'

y₂=y₁=0

At x₂=L,

y₂'= M₀L²+C₃

y₂'= y₁'= -M₀L/2

C₃= -3M₀L/2

y₂= -M₀L₂/2-(-3M₀L/2)+C₄

C₄= -M₀L

The equation of the electric curve is,

For AB:

y₁= (1/EI) [-M₀x₁³/6L  + M₀ Lx₁/6]

For CB:

y₂= (1/EI) [-M₀x₂²/2   + 3M₀Lx₂/2  - M₀L]

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A juice box is 5 cm long, 3 cm wide and
10 cm tall. The juice is poured into a
glass with a radius of 3 cm.
What is the depth of juice in the glass?
Answer in centimetres to 1 decimal place.

Answers

The depth of the juice in the glass is 5.30cm

Given in the question,

length of juice box = 5cm

width of juice box = 3cm

Height of juice box = 10cm

Volume of juice box = volume of cuboid = length× width× height

= (5)(3)(10)

=(15)(10)

= 150 cm³

This juice then poured into a glass with radius of 3 cm

Glass is of cylindric shape

So, volume of cylinder = πr²h

= π(3)²h

Volume of juice should be equal to volume of glass

=>  π(3)²h = 150 cm³

=> (3.14)(9)h=150

=> h = 150 / (3.14)(9)

h = 150/28.26

h = 5.30cm

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Prove that if n is an integer, then n 2 ≡ 0 or 1(mod 4).

Answers

Hence, we proved that if n is an integer, then either n= 2mod3 or n^2=n mod6.

In the given question we have to prove that prove if n is an integer, then either n= 2mod3 or n^2=n mod6.

If n=2mod3 then tere is nothing to prove.

If n≠ 2mod3 then either n=0mod3 or n=1mod3

Case (1)

n=0mod3 ⇒ 3 | n⇒n=3m for mϵZ

n^2-n=(3m)^2-3m

n^2-n=9m^2-3m

n^2-n=3m(3m-1)

So, 3|3m, in this case 3m is even or 3m-1 is even.

i.e. 2|3m(3m-1) and also 3|3m(3m-1)

⇒6|3m(3m-1)

⇒6|n(n-1)

⇒6|(n^2-n)

⇒n=n mod6 (Proved)

Case (2)

n=1mod3 ⇒ 3 | (n-1)⇒n=3m+1 for mϵZ

n^2-n=(3m+1)^2-(3m+1)

n^2-n=9m^2+6m+1-3m-1

n^2-n=9m^2+3m

n^2-n=3m(m+1)

So, 3|3m, in this case 3m is even or 3m+1 is even.

i.e. 2|3m(3m+1) and also 3|3m(3m+1)

⇒6|3m(3m+1)

⇒6|n(n-1)

⇒6|(n^2-n)

⇒n=n mod6 (Proved)

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The write question is

Prove that if n is an integer, then n = 2 mod 3 or n^2 = n mod 6.

which of the following is equivalent to sum from n equals 1 to infinity of 12 times quantity negative five eighths end quantity to the power of n question mark

Answers

The sum of given equation is 96/13.

Given equation is sum from n equals 1 to infinity of 12 times negative five eighths end quantity to the power of n that means

∑ n=1 to ∞ [12(-5/8)ⁿ]

This is in the form of geometric expression

that is an = ar^(n-1)

therefore we get

a = 12 and r = - 5/8

We have to find the sum.

Sum of infinity of the sequence is expressed as

Sum = a / (1-r)

where a  = first term of the series

and r = common ratio between two consecutive terms

Now we will substitute values of a and r in the above equation

Sum = [tex]\frac{12}{1-(-5/8)}[/tex]

        = [tex]\frac{12}{1 + 5/8}[/tex]

        = [tex]\frac{12}{13/8}[/tex]

Sum = [tex]\frac{96}{13}[/tex]

Hence the sum of given equation is 96/13.

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write a coordinate proof to prove that an arrowhead that is 3 inches long and 1.5 inches wide is an isosceles triangle. (5 points)

Answers

Answer:

(8,2), (12,2),(10,10)

Step-by-step explanation:

any coordinate that means the two sides will have the same length

first, we know that the length is twice the amount of the width

so any coordinate we pick must be twice the length

pick a coordinate that is quite high up ( so we don't get into negatives)

so let's say (10,10)

then we want to go a positive number down - don't want to deal with fractions.

so e.g 8

so 6 down would be (10,2)

then the width is half the length so it has a 4cm wide base

and put an equal amount on each side to the left and the right to get the base co-ordinates

to the left : (8,2)
plus to the right: (12,2)

2+2= make a 4cm base

put these coordinates together and presto! you have coordinated proofs!

Suppoe Jerome read the following number of page each day. Will he meet hi goal of reading at leat 85 page by the end of the day Friday?

Answers

If p = 6, he will not meet his goal.

If p = 7, he will meet his goal.

If p = 8, he will meet his goal.

What is inequality?

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

Here, we have

Jerome has already read 50 pages of a novel and read p pages each day from Monday to Friday.

If Jerome read at least 85 pages by the end of Friday, inequality will be,

50 + 5p ≥ 85

If Jerome reads 6 pages each day,

If p = 6,

Inequality will be,

50 + 5(6) ≥ 85

80 ≥ 85

It's not true.

Hence, he will not meet his goal.

If p = 7,

Inequality will be,

50 + 5(7) ≥ 85

85 ≥ 85

It's true.

Hence, he will meet his goal.

If p = 8,

Inequality will be,

50 + 5(8) ≥ 85

90 ≥ 85

It's true.

Hence, he will meet his goal.

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Dan emptied hi piggy bank and counted up how many coin he had. 14 pennie 12 nikle 32 dime 48 quarter 7 half dollar and 9 dollar coin how much are the coin from Dan' piggy bank worth in cent

Answers

The total value of Dan's piggy bank coins is worth 2844 cents.

What is currency?

Currency is defined as a unit of account that is issued by a government and is accepted at face value. Commodities and services can be exchanged using money.

As we know, each penny is worth 1 cent

Then, 14 pennies = 14 cents

And, a nickel worth 5 cents

Then, 12 nickles = 12*5 = 60 cents

And, a dime worth 10 cents

Then, 32 dimes = 32*10 = 320 cents

And, a quarter worth 25 cents

Then, 48 quarters = 48*25 = 1200 cents

And, a half dollar worth 50 cents

Then, 7 half dollars = 7*50 = 350 cents

And, a dollar worth 100 cents

Then, 9 dollars = 9*100 = 900 cents

Now,

Total coins worth = 14 + 60 + 320 + 1200 + 350 + 900

                             = 2844 cents

Hence, the total value of coins is 2844 cents.

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What is the distance from the center of the circle C to chord AB?

Answers

Answer:

Step-by-step explanation:

8.5

Can some one help me with this urgent?
Hotel Nights Price (in dollars)
A 3 192
B 5 300
C 7 455
Which hotel costs the least per night?

Answers

B costs the less because 300 divided by 5 equals $60 while A costs $64 and C costs $65
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