find the value of x ....

Yes, in a group of 2,000 people, at least 5 must have the same birthday.

This is due to the Pigeonhole Principle, which states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.

In this case, there are 2,000 people (the pigeons) and 365 possible birthdays (the pigeonholes). This means that, since 2,000 is greater than 365, at least 5 people must share the same birthday.

The Pigeonhole Principle states that if you have more items than boxes, then at least one box must contain more than one item. It can also be used to prove that certain problems have no solution.

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Complete Question:

In a group of 2,000 people, must at least 5 have the same birthday? Why?  Let X be the set of 2000 people (the pigeons) and Y the set of all possible birthdays (the pigeonholes). Define a function B: X - Y by specifying th B(x) = x's birthday. Now 2,000 > 4.366 = 1,464, and so by the generalized pigeonhole principle, there must be some birthday y such that B-1(y) has --Select- 4 + 1 = 5 elements. Hence at -Select- 5 people must share the same birthday.

Based on the definition of the angles of a straight line, the measure of the smallest angle is: are: 40°.

The sum of all the angles on a straight line is equal to 180 degrees.

To find the size of the smallest angle, find the value of a by creating the equation below:

(2a + 62) + (54 - a) + (5a - 20) = 180

Open the parentheses:

2a + 62 + 54 - a + 5a - 20 = 180

Combine like terms

6a + 96 = 180

6a = 180 - 96

6a = 84

6a/6 = 84/6

a = 14

Find the measure of each angles:

2a + 62 = 2(14) + 62 = 90°

54 - a = 54 - 14 = 40°

5a - 20 = 5(14) - 20 = 50°

The size of the smallest angle is 40°.

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The fraction 1¹/₂ + ⁵/₇ = 2³/₁₄

Fractions are numbers written in the form a/b where a and b are integers and b ≠ 0.

Since we have the fractions 1¹/₂ and  ⁵/₇ and we want to compute the sum

1¹/₂ + ⁵/₇, we re-write the first fraction as an improper fraction.

So, 1¹/₂ = ³/₂

Now, re-writting the equation, we have

³/₂ + ⁵/₇

To find the sum, wetake the L.C.M of both numbers which 2 × 7 = 14.

So, we make both denominators equal to the L.C.M.

So,  

³/₂ × ⁷/₇ + ⁵/₇ × ²/₂ = ²¹/₁₄ + ¹⁰/₁₄

= (21 + 10)/14

= 31/14

= (28 + 3)/14

= 28/14 + 3/14

= 2 + 3/14

= 2³/₁₄

So, 1¹/₂ + ⁵/₇ = 2³/₁₄

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The interest rate, to the nearest hundredth of a percent, which would be required in order for Grace to end up with $190 is 2.38%.

Mathematically, compound interest can be calculated by using this formula:

A(t) = P(1 + r)^{t}

Where:

Substituting the given parameters into the compound interest formula, we have;

190 = 140(1 + r)^{13}

190/140 = (1 + r)^{13}

1.3571 = (1 + r)^{13}

Taking the 13th root of both sides of the equation, we have:

[tex]\sqrt[13]{1.3571} = \sqrt[13]{(1 + r )^{13} }[/tex]

1.0238 = 1 + r

r = 1.02378 - 1

Interest rate, r = 0.0238

Interest rate, r = 2.38%

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The hyperbola's standard equation is [(x2/a2) - (y2/b2)] = 1, where X denotes the transverse axis and Y denotes the conjugate axis.

A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set. A hyperbola is made up of two mirror images of one another that resemble two infinite bows. These two sections are known as connected components or branches. A hyperbola is a geometric shape in mathematics where the difference between the lengths from any point on the figure to two fixed locations is a constant (the Greek letter o literally means "overshooting" or "excess"). We refer to the two fixed spots as foci (plural of focus).

Given

The equation for the hyperbola

The hyperbola's standard equation is [(x2/a2) - (y2/b2)] = 1, where X denotes the transverse axis and Y denotes the conjugate axis.

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Answer:

Below

Step-by-step explanation:

Primes under 25      2 3 5 7 11 13 17 19 23

   5 7 13

    7  7   11    ( can we use numbers twice?)

         you can look for more....but that may be it ....

Answer:

x = -0.8.

Step-by-step explanation:

To solve for x in the equation g(x) = 10, we need to find the value of x that makes g(x) equal to 10. Since we are given that g(x) = 2/x+1, we can substitute this expression for g(x) in the equation g(x) = 10 to get:

2/x+1 = 10

Next, we can multiply both sides of the equation by x+1 to get rid of the fraction on the left side:

2 = 10 * (x+1)

This simplifies to 2 = 10x + 10, which we can rearrange to get 2 - 10 = 10x. Subtracting 10 from both sides gives us -8 = 10x. Finally, dividing both sides by 10 gives us the solution: x = -0.8.

Therefore, the value of x that makes g(x) equal to 10 is x = -0.8.

Richard will increase the amount of time he studies each night by 25%.

The percentage is defined as a ratio expressed as a fraction of 100.

To find the percentage increase, we need to first find the difference between the two amounts of time.

In this case, the difference is 50 minutes - 40 minutes = 10 minutes.

Next, we need to divide the difference by the original amount of time and multiply by 100% to express the answer as a percentage.

In this case, the percentage increase is :

⇒ (10 / 40) x 100% = 25%.

Therefore, he will increase the amount of time he studies each night by 25%.

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Here, in the given equation it is true because two different sign, and the result is negative.

To multiply or divide signed integers, always multiply or divide the absolute values and use these rules to determine the sign of the answer.

When multiply two integers with the same signs, the result is always positive. Just multiply the absolute values and make the answer positive.

When multiply two integers with the different signs, the result is negative.

Here in this equation,

20 ÷ (-5)

= - 4

So, it is true.

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Answer:

72% are black haired - 5 students becomes 65% students are black haired.

meaning 7% are 5 students

Base = Percentage/Rate

Base = 5/0.07

Base = 71 students

71 (students) * 0.72 (rate of black haired) = 51

51 - 5 (leave the class) = 46 students

71 (students) * 0.65 (rest of black hair) = 46 students

Step-by-step explanation:

The rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled is 11 feet .

Slope and rate of change are the same thing. The difference is just semantics of the situation.

Typically we use the word “slope” when we are referring to a graph, and we use the phrase “rate of change” when we are referring to a table or a situation in real life.

But that’s not absolute. We can count the slope on a graph, but there’s also a “slope formula” for use when you have two coordinate points or two data points — even though you are not creating a graph.

It is the derivative of of the slope, or the second derivative of the original function.

For example, if you plot position verses time, the slope between two points(change in position per change in time) is the velocity. This is the first derivative.

Take any two points ( 0 , 380 ) and ( 15 , 545 )

slope m = 545 - 380 / 15 - 0

= 165 / 15

= 33 / 3

= 11 / 1

= 11 feet

Hence the slope m is 11 feet .

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Answer:

0.63 kg

Step-by-step explanation:

KE = 1/2mv²

solve for m:

m = 2(KE)/v²

m = 2(140J) / (21m/s)²

m = 280J / 441 = 0.63 kg

Answer:

Step-by-step explanation:

You want to solve the given system of equations by eliminating the y-term. You also want to know what constants are used in the process.

The y-term can be eliminated from these equations by combining them in such a way as to may the coefficient of y be zero. This can be done an infinite number of ways.

One way that works reasonably well is to identify the coefficients of y, and multiply each equation by the y-coefficient in the other equation. The resulting equations can be subtracted one from the other to eliminate the y-terms, which now have identical coefficients. You can choose the equation with the smaller x-coefficient to subtract from the other one.

The y-term coefficients are 2 and 3.

Multiply the first equation by 3, and the second by 2.

  3 × (2x +2y) = 3 × 7   ⇒   6x +6y = 21

  2 × (6x +3y) = 2 × (-2)   ⇒   12x +6y = -4

The x-coefficients are 6 and 12. We choose to subtract the first equation (with x-coefficient 6) from the second equation:

  (12x +6y) -(6x +6y) = (-4) -(21)

  6x = -25 . . . . . . . . simplified

  x = -25/6 = -4 1/6 . . . . . divide by 6

Substituting for x in the first equation, we have ...

  2(-25/6) +2y = 7

  2y = 7 +25/3 . . . . . add 25/3

  2y = 46/3 . . . . . . . .combine terms

  y = 23/3 = 7 2/3 . . . . divide by 2

The solution to the equations is (x, y) = (-4 1/6, 7 2/3).

Since these numbers are not integers, we choose to check them in the original equations. We used the first equation to find y, so we'll use the second equation for checking.

   6(-4 1/6) +3(7 2/3) = -25 +23 = -2 . . . . . . as required

__

Additional comment

If you solve these by addition, rather than subtraction, you want to choose multipliers that result in opposite coefficients, so they add to zero. Essentially, you use the opposite coefficients, as described above, but you negate one of them.

Above, we chose the subtraction in a way that resulted in the x-coefficient being positive. If you arbitrarily choose the signs of the multipliers (always negating the second one, for example), the combined equations may make the x-coefficient negative. That works, too, but may require more mental effort to deal with the minus sign.

Of course, you can use the x-coefficients and eliminate the x-terms.

Or, you can use a single multiplier that corresponds to the ratio of the coefficients. For example the ratio of the 2nd y-coefficient to the first one is 3/2. Multiplying the first equation by this will give the y-term a coefficient of 3, matching the y-coefficient in the 2nd equation. Then the subtraction can proceed as already described.

  (6x +3y) -3/2(2x +2y) = (-2) -3/2(7)

  3x = -25/2 . . . . . simplified; y is gone.

Answer:

B. 8

Step-by-step explanation:

I’m glad to help you

Answer:

801 boxes

Step-by-step explanation:

[tex]\frac{7209}{9}[/tex] = 801

Answer:

37.237%

Step-by-step explanation:

Use the Formula I = P x R x T

P = Principal amount (the beginning balance).

R = Interest rate (usually per year, expressed as a decimal).

T = Number of time periods (generally one-year time periods).

Plug in the values

I = 5305 x R x 20

Solve for R by dividing 20 by 5305

I=5305 x R x 20

20 / 5305 = 0.0037

Answer: 10.56 or 10.6 %

Step-by-step explanation:

5305 x x^20 = 39534

39534/5305 = x^20

20√39534/5305 = x

x = 1.1056

1.1056 x 100 = 110.56

110.56 - 100 = 10.56 or 10.6

Answer: 10 pieces

Step-by-step explanation:

Answer:

10 ropes

Step-by-step explanation:

5 divided by 1/2 is 10

Answer:

Θ = 49.6°

Step-by-step explanation:

cos Θ = adj/hyp

cos Θ = 24/37

cos Θ = 0.64864

Θ = cos^-1 0.64864

Θ = 49.6°

a) The monthly payment for each loan individually is as follows:

                                 Loan A        Loan B         Loan C          Total

Monthly payments $133.82        $188.18      $195.00      $517.00

b) The total payments during the life of all three loans is $105,060, classified as follows:

                                 Loan A        Loan B         Loan C          Total

Total amount          $27,300     $49,680     $28,080    $105,060

c) The monthly payments after consolidating the three loans are $350.69.

d) The total payments over the 22 years period will be $92,581.47.

Note that student loans attract simple interest and not compound interest.

After the bank consolidates it, the interest system changes to compounding.

The total interest is computed by applying the annual percentage rate (APR) to the principal and the loan term.  The result is added to the principal to obtain the total payment for each loan.

The total payment is divided by the loan period to get the monthly payments.

But for the consolidated loan by the bank, we can use an online finance calculator to determine the monthly payments and total payment over the loan term as follows.

                                 Loan A        Loan B         Loan C          Total

Student loan            $12,000      $18,000       $13,500     $43,500

APR                             7.5%               8%              9%

Loan term                 17 years      22 years     12 years

Period in months        204              264           144

Total interests         $15,300      $31,680       $14,580      $61,560

Total amount          $27,300     $49,680     $28,080    $105,060

Monthly payments $133.82        $188.18      $195.00      $517.00

Total amount of loans = $43,500 ($12,000 + $18,000 + $13,500)

Bank APR = 8%

Loan term = 22 years

N (# of periods) = 264 months (22 years x 12)

I/Y (Interest per year) = 8%

PV (Present Value) = $43,500

FV (Future Value) = $0

Results:

PMT = $350.69

Sum of all periodic payments = $92,581.47

Total Interest = $49,081.47

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The solution to the system of equations, y = 4x - 9 and y = x - 3, is: (2, -1)

The coordinates of the ordered pair that will make both equations true is the solution to the system.

Given the linear equations as:

y = 4x - 9 --> equation 1

y = x - 3 --> equation 2

Make both linear equations equal to each other and find the value of x. Thus:

4x - 9 = x - 3

Combine like terms

4x - x = 9 - 3

3x = 6

Divide both sides by 3

3x/3 = 6/3

x = 2

To find the value of y, substitute x = 2 into equation 1:

y = 4(2) - 9

y = 8 - 9

y = -1

The solution is, (2, -1).

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The function f is guaranteed by the extreme value theorem to have an absolute maximum and an absolute minimum on the closed interval a. [-5, 5].

The extreme value theorem states that if a function f is continuous on a closed interval [a, b], then it must have both an absolute maximum and an absolute minimum on that interval. Since the function f is given as being defined on the closed interval [-5, 5], it must have both an absolute maximum and an absolute minimum on this interval.

We can check that the function f is continuous on the interval [-5, 5] as follows:

First, we need to check that the function is defined at every point in the interval. The function f is defined as f(x) = x+4/(x-1)(x+3). The only points at which this function is not defined are x = 1 and x = -3, which are not within the interval [-5, 5]. Therefore, the function is defined at every point in the interval.

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Answer:

15.

Step-by-step explanation:

The common ratio = 60/120 = 1/2

So the next term is 30 * 1/2 = 15.

The region bounded by the equations has a precise area of 21.33 units.

A boundary or some set of constraints are imposed on a bounded region. To put it another way, the size of a bounded shape cannot be infinite. Anything that is bound must be able to be contained within certain parameters.

x2 = 4y2 from equation (1), y3 = 4y2 y3 - 4y2 = 0 y2(y - 4) = 0 y2 = 0 or y-4 = 0 or y = 4 These will be our integration bounds. We have given that x2 = y3 --------- (1) and x = 2y --------- (2).

Therefore, we will express area as A = [- 4]04 = [- 4 - 0] = 64 - 85.33 A = -21.33, or A = 21.33. This indicates that the area of the bounded region is 21.33 units.

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The product of the given values would be = 1,125. That is option A.

Multiplication is defined as one of the major arithmetic operation along with others such as addition, subtraction and division which is used to to determine the product of two or more values.

The rule of multiplication is that

Therefore;

= (-25)× (15) × (-3)

= -375 × -3

= 1,125.

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Answer:

Step-by-step explanation:

Evan bought 18 postcards in 9 days

since he got 12 in 6 days that means he got 2 each day so 9x2=18

or if you add up by 2 9 times you would get 18 :)

Reagan will grow 1/2 inch than her brother if Reagan grew 9/10 of an inch and her brother grew 2/5 of an inch by using ratio and proportion concept,

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion. For instance, if there is 1 boy and 3 girls, the ratio would be written as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.

A: b a/b is the ratio formula, which may be used to calculate any two values. A:b::c:da:b::c:da, on the other hand, is how the percentage formula is written.

Given,

The height grown by Reagan=9/10 inch

The height grown by Reagan brother=2/5 inch

(9/10)-(2/5)

=1/2 inch

Therefore, Reagan will grow 1/2 inch than her brother.

Therefore,

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The Option that can be proven is:

Definitions, assertions, and methods are linked in a proper fashion to get the desired outcome in mathematical proof.

This procedure helps pupils understand the rationale behind the statement. This is also true of counterexamples and their important significance in mathematics.

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TU with endpoints T(1,2) and U(4,6) and its images after the composition are T' = (-1, -1) and U' = (2,3) and T'' = (-3, 7) and U'' = (0,11).

Tradition holds that the reflection of point P across the line, denoted by the word P', is the "image" of point P. (pronounced "P prime").

Given, line TU with endpoints T(1,2) and U(4,6).

To find the translation:

In 1:

Translate TU 2 units left and 3 units down.

That means,

T' = (-1, -1) and U' = (2,3)

In 2:

Translate TU 4 units left and 5 units up.

That means,

T'' = (-3, 7) and U'' = (0,11)

Therefore, the image points are T' = (-1, -1) and U' = (2,3) and T'' = (-3, 7) and U'' = (0,11)

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Total 26, 250 passengers are flew in June in an airline flights between Chicago and Denver .

An Equations with roots , such as the square root cannot be solved until its root is eliminated. Once we have isolated the square root on one side, we can eliminate it by raising both sides of the equation to powers equal to the square root. For example, if the square root is only one-sided, we can square both sides. We have , An airline offers daily flights between Chicago and Denver. Cost function of flight is,

C = 0.2x + 1

where x represents the number of passengers (in thousands) in flight.

To calculate how many passengers flew each day in June, we need to set the function to 2.5 (since the cost is in millions of dollars) and solve for the variables. This means taking the square root equal to 2.5. Therefore, to solve for the variables contained in its square root, we need to square both sides. This process and solution are described below,

√(0.2x + 1) = 2.5

Squaring both sides

=> (√(0.2x + 1) )² = ( 2.5 )²

=> 0.2x + 1 = 6.25

=> 0.2 x = 6.25 - 1 = 5.25

=> x = 5.25/0.2

=> x = 26.25

Now, we know that our variable i.e x measures passengers in thousands, so total passenger flew in June are 26.25 × 1000 = 26, 250 .

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