Verify that phi(x) = 2/(1 - ce^x), where c is an arbitrary constant, is a one-parameter family of solutions to dy/dx = y(y - 2)/2. Graph the solution curves corresponding to c = 0, plus or minus 1, plus or minus 2 using the same coordinate axes.

The ordered pair (1, 2) is not included in the solution set to the system of inequalities y < x^2 + 3 and y > x^2 - 2x + 8.

To determine which ordered pair is included in the solution set to the given system of inequalities, we need to evaluate each ordered pair by substituting the values into the inequalities and checking if they satisfy the conditions.

Let's consider the ordered pair (1, 2) as a candidate solution:

Substituting x = 1 and y = 2 into the first inequality:

2 < 1^2 + 3

2 < 4 (True)

Substituting x = 1 and y = 2 into the second inequality:

2 > 1^2 - 2(1) + 8

2 > 1 - 2 + 8

2 > 7 (False)

Since the second inequality is not satisfied, the ordered pair (1, 2) is not included in the solution set to the given system.

Therefore, the ordered pair (1, 2) is not included in the solution set.

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The answer is 1.86.

1.86 × 10^0 is equivalent to 1.86 x 1 = 1.86

In this context, the term 10^0 is referred to as an exponent.

An exponent is a mathematical operation that indicates the number of times a value is multiplied by itself.

A number raised to an exponent is called a power.

In this instance, 10 is multiplied by itself zero times, resulting in one.

As a result, 1.86 × 10^0 is equivalent to 1.86.

Therefore, the answer is 1.86.

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(a) The amount in the account at the end of 1 year is $3330

(b) The amount in the account at the end of 2 year is $3696.3

It is given that Deon deposit $3000 that pays 11% interest compounded each year .

(a) Putting P = $3000, R =  11%  , T = 1 year in equation (1) , we get

           \(A=3000(1+\frac{11}{100} )^1\\\\A=3000(1+0.11)\\A=3000(1.11)\\A=3330\)

(b) Putting P = $3000, R =  11%  , T = 2 year in equation (1) , we get

       \(A=3000(1+\frac{11}{100} )^2\\\\A=3000(1+0.11)^2\\A=3000(1.11)^2\\A=3000\times1.23\\A=3696.3\)

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The given path can be illustrated in the following diagram:

She has only 30 miles worth of gas, if she comes back through the same path then the total distance is:

Therefore, she has not enough gas to go back using the same path.

Now, the total distance traveled in a straight path (SP) can be found using the Pythagorean theorem, we get:

Therefore, she needs to take a straight path.

Answer:

5x + 6y = -10

Step-by-step explanation:

(-2, 0) and (-8, 5)

m = (y₂ - y₁) /  (x₂ - x₁)

m = (5 - 0) / (-8 -(-2)

m = 5 / (-8+2)

m = -5/6

y = mx + b

(-8, 5)

5 = -5/6(-8) + b

5 = 40/6 + b

b = 5 - 40/6

b = -5/3

y = mx + b

y = -5/6x - 5/3           *6

6y = -5x -5(2)

6y = -5x - 10

5x + 6y = -10

The Percentage of female students in the school trip is 39%.

According to the statement

we have given that the some ratio of the class students and teachers and we have to find the percentage of female students on the school trip.

So, For this purpose,

The Given information is:

The ratio of the number of teachers to the number of students is 1:15.

and the ratio of the number of male and female students is 7:5

Suppose the number of teachers is x. So, students become 15x

For the ratio of male to female, assume male is 7y, so female is 5y

The sum of the male and female students comprises the whole student community is:

15x = 7y + 5y

15x = 12y

5x = 4y

then

The percentage of female students on the trip is calculated by use the below written formula. So,

Percentage of female students = (5y / x +15x) * 100

Percentage of female students = (5y /16x) * 100

Substitute the value of y which is y = 5/4x

So,

Percentage of female students = (5*5/4x / 16x) * 100

Percentage of female students = 625/16

Percentage of female students = 39%.

So, The Percentage of female students in the school trip is 39%.

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Answer:

(-1,-1)(4,-20)(2,0)

Step-by-step explanation: Just fill in the x and y

The side lengths on the similar polygons are given as follows:

Similar polygons are polygons that share these two features presented as follows:

Considering the equivalent side lengths, the proportional relationship for the side lengths in this problem is given as follows:

18/16 = 18/EI = ST/24.

Hence the length of EI is given as follows:

EI = 16.

The length of ST is obtained as follows:

18/16 = ST/24

16ST = 18 x 24

ST = 18 x 24/16

ST = 27.

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Answer:

Step-by-step explanation:

4a

The approximate value of the probability of three or more errors in 106 digits by using the Poisson distribution approximation is 0.393.

Given data; Error probability, p = 10^(-6) Probability of no error in 10^6 digits, P(no error) = 1 - p = 1 - 10^(-6) = 0.999999

The exact value of the probability of three or more errors in 10^6 digits;

Using binomial distribution; Total number of trials, n = 10^6Probability of success, p = 10^(-6)

Probability of failure, q = 1 - p = 1 - 10^(-6) = 0.999999

The random variable x = number of errors in n trials = 0, 1, 2, 3, .... , n

The probability mass function of the binomial distribution is;

P(x) = ( nCx ) * (p^x) * (q^(n-x))

Where, nCx = n! / x! (n-x)!

P(3 or more errors) = P(x ≥ 3) = P(x = 3) + P(x = 4) + P(x = 5) + ..... + P(x = n)P(x = 3) = ( 10^6 C 3 ) * (10^(-6))^3 * (0.999999)^10^6-3P(x = 4) = ( 10^6 C 4 ) * (10^(-6))^4 * (0.999999)^10^6-4P(x = 5) = ( 10^6 C 5 ) * (10^(-6))^5 * (0.999999)^10^6-5......P(x = n) = ( 10^6 C n ) * (10^(-6))^n * (0.999999)^10^6-n

To find this probability, we need to evaluate these probabilities. But evaluating such a large number of probabilities is a very difficult task. So, we use Poisson distribution to approximate this binomial distribution. Approximate value of the probability of three or more errors in 10^6 digits by using the Poisson distribution approximation;

In Poisson distribution, λ = np

The random variable x = number of errors in n trials = 0, 1, 2, 3, ....

The probability mass function of Poisson distribution is;

P(x) = ( e^(-λ) ) * (λ^x) / x!

Here,

λ = np = 10^6 * 10^(-6) = 1P(x ≥ 3) = P(x = 3) + P(x = 4) + P(x = 5) + .....P(x) = ( e^(-1) ) * (1^x) / x!P(x = 3) = ( e^(-1) ) * (1^3) / 3! = 0.0613201P(x = 4)

= ( e^(-1) ) * (1^4) / 4! = 0.0153300P(x = 5) = ( e^(-1) ) * (1^5) / 5! = 0.003065662......P(x ≥ 3) = 0.0613201 + 0.0153300 + 0.003065662 + .....

= 1 - {P(x = 0) + P(x = 1) + P(x = 2)}

= 1 - [ ( e^(-1) ) * (1^0) / 0! + ( e^(-1) ) * (1^1) / 1! + ( e^(-1) ) * (1^2) / 2! ]

= 1 - [ ( 1 / e^1 ) + ( 1 / e^1 ) + ( 1 / 2e^1 ) ]

= 1 - [ ( 2 + 1 ) / 2.7183 ]

= 1 - 0.607

= 0.393 (approx.)

Therefore, the approximate value of the probability of three or more errors in 106 digits by using the Poisson distribution approximation is 0.393.

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We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.

The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.

`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`

As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `

lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`

Since the limit of the ratio test is less than one, the given series converges.

The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).

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The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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The value of the car will decrease by 8% each year, so after one year, its value will be 92% of $34,000, which is $31,280.

After two years, it will be 92% of $31,280, which is $28,777.60. Similarly, after three years, the value will be $26,467.49, and after four years, it will be $24,345.71. The predicted value of the car four years from now, considering its 8% annual depreciation rate, is $24,345.71. The value decreases each year by multiplying the previous year's value by 0.92, representing a 92% retention. Therefore, the car's value is estimated to depreciate to approximately 71.9% of its initial value over the four-year period. An estimate is an approximate calculation or prediction of a particular value or quantity. It is an educated guess or an informed assessment based on available information and assumptions. Estimates are commonly used in various fields, including finance, statistics, engineering, and planning.

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Answer:

27.15

Step-by-step explanation:

Let us name the vertices as shown below

A(- 1, 6)

B(5, 1)

C(- 4, - 3)

We would calculate the distance between each vertex by applying the formula for calculating distance between 2 points. It is expressed as

The perimeter of the triangle is the sum of the length of each side. Thus,

Perimeter = 7.81 + 9.85 + 9.49

Perimeter = The perimeter of the triangle is the sum of the length of each side. Thus,

Perimeter =   27.15



0.29 km is equal to 290,000 mm when rounded to two significant figures.

Convert kilometers to millimeters, you need to multiply the given value by a conversion factor. In this case, since there are 1,000 meters in a kilometer and 1,000 millimeters in a meter, the conversion factor is 1,000,000 (1,000 x 1,000).

Step 1: Multiply 0.29 km by the conversion factor:

0.29 km x 1,000,000 = 290,000,000 mm

Step 2: Round the result to two significant figures:

Since the original value, 0.29 km, has two significant figures, we round the result to match.

290,000,000 mm becomes 290,000 mm.

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Step-by-step explanation:

vertex             vertical angles

Answer:

$16

Step-by-step explanation:

He received that much money because all you have to do is just subtract            

43-27. Then thats how I got my answer.

Hope this helps and have a great day!

Answer:

Willie received $16 dollars during the weekend

Step-by-step explanation:

$43 (how much money he has now) - $27 (how much he had last Friday) = $16 (how much he received while babysitting during the weekend)

Answer:

While the title was not in general use until much later, Martha Washington, the wife of George Washington, the first U.S. president (1789–1797), is considered to be the inaugural first lady of the United States. During her lifetime, she was often referred to as "Lady Washington".

plz can i get brainliest

Answer:

there are many first lady's but because you said was like past tense the last first Lady was Melania Trump. the current first Lady is Jill Biden! I hope this helps!!♡♡

Answer:

If an atom has the same number of protons and electrons then it is electrically neutral. Not all atoms have to have the same number of atoms because the number of electrons can be changed with the element remaining the same. Protons have a positive charge while electrons have a negative charge. The net charge is dependent on the number of protons and electrons. If it has more protons it would have a higher amount of positive charge therefore making it a positive net charge. The same thing applies with electrons just opposite.

If the atom has no charge (neutral) then there are the same number of protons and electrons. The positive protons cancel out with the negative electrons to produce this neutral state. We can say the net charge is 0 here.

Now if you take away one or more electrons, then there will be more positive protons to outnumber the negative electrons. Overall, the net charge will be positive. For example, if the atom loses 3 electrons, then you'll have a net charge of \(3^{+}\). These positively charged ions are known as cations. You pronounce this as "cat-ion" instead of "catshun".

On the flip side, if you add electrons to an atom, then you'll make the net charge overall to be negative. So let's say we add 4 electrons. We'll have the net charge be \(4^{-}\) and this is an anion. To pronounce "anion" you would say "an ion" instead of "anyun".

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

In short, the number of protons and electrons are the same if the net charge is 0 and we're not dealing with ions. If you are dealing with ions, then the two counts will not be the same. Note how in the examples above, I didn't change the number of protons. Doing so would change the overall element entirely.

Answer:

y=3x-13

Step-by-step explanation:

Since the parallel equations have equal slope.

The equation of line parallel to y=3x+7 will be y=3x+k.

(4,-1) lies in the line so it satisfies the equation amd we get the value of k as -13 and finally we substitute the value of k in the eqn and we finally get the equation as 3x-y-13=0 or you can also write it as y=3x-13

Answer:

b is the answer okkkkkkkkkkkkkkkk

Answer:

plates shifting continental drift

Answer:

Rotate Each dot in the proper way each right angle is 90 Degrees

Step-by-step explanation:

Rotate the Coordinates

pretty simple

Step-by-step explanation:

in probability,or means addition.

14/28+19/28

1/2+19/28

you then find the LCM of the denominator.

14+19/28

33/28

you then divide 33 by 28.

Step-by-step explanation:

adding all it will be

19/30 in exact form

Answer:

X = 12.645 round to 12.7

Step-by-step explanation:

∆LMN ~ ∆OPQ

so the coresponding side ratio are proportional

LM/OP = LN/OQ

LM/OP = LN/OQ49/OP = 31/8 ... the u solve x

X = 12.645 round to 12.7

Correct option is B, function for the area of the circle in terms of the side of the square is A = \(\pi \frac{S^2}{4}\).

Because the area of a square is one of its sides multiplied by itself, the area equals the square of the radius of a circle multiplied by two. Because the radius of the circle is a known quantity, the area of the inscribed square can be calculated numerically.

An “inscribed” square in a square is one in which all of the vertices of the smaller square are on the borders of the bigger square. To do this, the vertices of the smaller square will split each side of the bigger square into two segments, one on each side.

If a square is used to inscribe a circle, the square's side length will match the circle's diameter. As a result, the radius of an inscribed circle is S/2 for a square with length S. hence, the area of a circle is expressed as the square's sides,

= \(\pi \frac{S^2}{4}\)

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After evaluating the algebraic expression we can infer that both students were correct.

An algebraic expression in mathematics is one that was produced utilizing integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

On the other hand, transcendental numbers, such and e, are not algebraic because they are not generated from integer constants and algebraic operations. While the definition of e necessitates an infinite number of algebraic operations, the creation of is frequently done as a geometric expression .

If an expression can be converted into a rational fraction using the characteristics of the arithmetic operations, it is said to be rational expression (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).

The expression 5a/2a+3 is the quotient of the terms as it can be written as 5a ÷ ( 2a+3 ).

Again the expression 2a +3 is a sum with only two terms.

Hence both students were correct.

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After evaluating the algebraic expression we can infer that both students were correct.

An algebraic expression in mathematics is one that was produced utilizing integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

On the other hand, transcendental numbers, such and e, are not algebraic because they are not generated from integer constants and algebraic operations. While the definition of e necessitates an infinite number of algebraic operations, the creation of is frequently done as a geometric expression .

If an expression can be converted into a rational fraction using the characteristics of the arithmetic operations, it is said to be rational expression (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).

The expression 5a/2a+3 is the quotient of the terms as it can be written as 5a ÷ ( 2a+3 ).

Again the expression 2a +3 is a sum with only two terms.

Hence both students were correct.

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