the given family of functions is the general solution of the differential equation on the indicated interval. find a member of the family that is a solution of the initial-value problem. y

Answer:

Step-by-step explanation:

Find the Inverse y=2x. y=2x y = 2 x. Step 1. Interchange the variables. x=2y x = 2 y. Step 2. Solve for y y

Answer: The inverse of the function y = 2x2 + 2 is f-1(x) = √(x - 2) / √2.

Answer:

x = 27

Step-by-step explanation:

AOB is a straight angle = 180°

the 3 angles on it therefore sum to 180° , that is

36 + 90 + 2x = 180

126 + 2x = 180 ( subtract 126 from both sides )

2x = 54 ( divide both sides by 2 )

x = 27

The equations with parentheses added to make them true are;

Parentheses indicate that operations within it should be completed first before those that are outside the parentheses.

The given terms of the equations can be regrouped with parentheses to make the equations true as follows;

1. 4 × 3 + 7 - 6 × 1 + 4 = 20

The above equation gives;

3 + 7 - 6 = 4

Therefore;

4 × 3 + 7 - 6 × 1 + 4 = 4 × (3 + 7 - 6) × 1 + 4

4 × (3 + 7 - 6) × 1 + 4 = (4 × 4) × 1 + 4

(4 × 4) × 1 + 4 = 16 × 1 + 4 = 16 + 4 = 20

Which gives;

2. 60 - 18 ÷ 2 + 4 + 10 ÷ 2 = 12

60 - 18 = 42

2 + 4 = 6

The first four terms, therefore gives;

(60 - 18) ÷ (2 + 4) = 7

10÷2 = 5

Which gives;

60 - 18 ÷ 2 + 4 + 10 ÷ 2 = (60 - 18) ÷ (2 + 4) + 10÷2

(60 - 18) ÷ (2 + 4) + (10÷2) = 7 + 5 = 12

Which gives;

60 - 18 ÷ 2 + 4 + 10 ÷ 2 = (60 - 18) ÷ (2 + 4) + 10÷2 = 12

The expression is therefore;

3. 80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 44

80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 80 - 36 ÷ (2 + 6 - 2) × (5 + 1)

(2 + 6 - 2) = 6, and (5 + 1) = 6

Therefore;

80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 80 - ((36 ÷ 6) × 6)

80 - ((36 ÷ 6) × 6) = 80 - ((36 × 6) ÷ 6)

80 - ((36 × 6) ÷ 6) = 80 - (36 × 1) = 44

Therefore;

4. 3 × 5 + 4 - 2 × 2 + 6 - 4 = 15

3 × 5 + 4 - 2 × 2 + 6 - 4 = 3 × (5 + 4) - (2 × (2 + 6) - 4)

3 × (5 + 4) - (2 × (2 + 6) - 4) = 3 × 9 - (16 - 4)

3 × 9 - (16 - 4) = 27 - 12 = 15

Therefore;

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Answer:

g(x) = |x + 3|

g(x) is nonnegative on all real numbers.

g(x) is decreasing on x <= -3 and increasing on x >= -3.

As x tends to negative infinity, g(x) tends to positive infinity.

As x tends to positive infinity, g(x) tends to positive infinity.

Domain: all real numbers

Range: all nonnegative real numbers

note that parallel lines have equal gradients.

give the line 2x+3y =5 write it in the form y=mx+c first so that you can be able to know its gradient. Mind you getting the gradient of the given line means finding the gradient of the new equation because they are equal as stated above.

[tex]2x + 3y = 5 \\ 3y =5 - 2x \\ \frac{3y}{3} = \frac{5}{3} - \frac{2x}{3} \\ y = \frac{5}{3} - \frac{2}{3} x[/tex]

FROM THE GIVEN EQUATION WE CAN NOW SEE THAT THE GRADIENT IS

[tex] - \frac{2}{3} [/tex]

Meaning the gradient of the new EQUATION sknce it is parallel to the given one will be

[tex]m = - \frac{2}{3} [/tex]

also.

given the points we can substitute to get the value of the unknown c.

[tex] - 1= - \frac{2}{3} (3) + c \\ - 1 = -2 + c \\ c = - 1 + 2 \\ c = 1[/tex]

[tex]y = - \frac{2}{3} x + 1[/tex]

The vertex of the equation is (1, -1).

The equation of a parabola in vertex form is,

y = a(x-h)² + k

The coordinates of the vertex are (h,k) respectively and a is a constant.

Given:

y =  x² - 2x

Rearrange the given equation in the form of the equation of the parabola in vertex form using the method of completing the square.

y = (x² - 2x + 1) - 1

y = (x - 1)² - 1

Therefore, the vertex of the equation is (1, -1).

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Answer: v = 17°

Step-by-step explanation:

All triangles add up to 180°.

[tex]94+35+3v=180[/tex]

[tex]3v=51\\v=17[/tex]

Answer:

Step-by-step explanation:

v=51

The parameters are ΔUVW with side UW extended to X then m ∠UVW = (3x + 4)°, m ∠VWX = (8x -12)° and m ∠WUV = (x + 20)° then the value of x = 9°.

The given parameters exist;

ΔUVW with side UW extended to X

m ∠UVW = (3x + 4)°, m ∠VWX = (8x -12)° and m ∠WUV = (x + 20)°

We have that m ∠UVW + m ∠WUV + m ∠VWU = 180° (Sum of the interior angles of a triangle theorem)

Therefore, m ∠VWU = 180° - (m ∠UVW + m ∠WUV)

Also, we have that m ∠VWX and m ∠VWU exist supplementary angles, (The sum of angles on a straight line)

∴ m ∠VWX + m ∠VWU = 180° (Definition of supplementary angles)

m ∠VWU = 180° - m ∠VWX

∴ m ∠VWX = (m ∠UVW + m ∠WUV)

Substituting the values in the above equation, we get;

(8x -12)° = (3x + 4)° + (x + 20)°

simplifying the above equation, we get

8x - 3x - x = 4 + 20 + 12

4x = 36

x = 36/4 = 9

Therefore, the value of x = 9°.

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The price of an adult ticket and a student ticket is $14 and $8, respectively.

Using algebraic expression and equation, we can express each statement and determine the price of each ticket.

Let x = the price of an adult ticket

y = the price of a student ticket

If on the first day of ticket sales, the school sold 3 student tickets and 1 adult ticket for a total of $38, then we can express this as:

3y + x = 38     (equation 1)

If the school took in $52 on the second day by selling 3 student tickets and 2 adult tickets, then we can express this as:

3y + 2x = 52     (equation 2)

3y + 2x = 52     (equation 2)

-(3y + x = 38)    (equation 1)

x = 14

Substitute the value of x in any of the two equations.

3y + x = 38     (equation 1)

3y + 14 = 38

3y = 38 - 14

3y = 24

y = 8

price of an adult ticket = $14

price of a student ticket = $8

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The output value of h( 2 ) in the function h( x ) = 4x + 4 is 12.

A function is a relationship that maps one input to one output, for a relation to qualify as a function, each of its x-value can only have one y-value.

Given the data in the question;

To solve for the output value of h( 2 ), replace all the occurrence of x with 2 in the function and simplify.

h( x ) = 4x + 4

h( 2 ) = 4( 2 ) + 4

Multiply 4 and 2

h( 2 ) = 8 + 4

Add 8 and 4

h( 2 ) = 12

Therefore, the output value is 12, this forms an ordered pair of (2,12) on the graph.

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The answers to all the subparts are given below:

So, (A) Chebyshev's theorem is used:

So,

Therefore, the minimum proportion of commuters who are within two standard deviations of the mean is:

(B) Minimum percentage of commuters in the city has a commute time within 1.5 standard deviations of the​ mean:

Here, k = 1.5

Consequently, the shortest commute within two standard deviations of the mean is:

Within 1.5 standard deviations, commute times:

(C) Minimum percentage of commuters who have commute times between 6 minutes and 48.6 ​minutes:

So,

Therefore, the answer to all the subparts are given below:

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The correct question is given below:
The mean commute time to work for a resident of a certain city is 27.3 minutes. Assume that the standard deviation of the commute time is 7.1 minutes to complete parts​ (a) through​ (c).

​(a) What minimum percentage of commuters in the city has a commute time within 2 standard deviations of the​ mean?

nothing​% ​(Type an integer or a​ decimal.)

​(b) What minimum percentage of commuters in the city has a commute time within 1.5 standard deviations of the​ mean? What are the commute times within 1.5 standard deviations of the​ mean?

The minimum percentage of commuters in the city that has a commute time within 1.5 standard deviations of the mean is nothing​%. ​(Round to one decimal place as​ needed.)

The commute times within 1.5 standard deviations of the mean are between nothing and nothing.

​(Type an integer or a decimal. Use ascending​ order.)

​(c) What is the minimum percentage of commuters who have commute times between 6 minutes and 48.6 ​minutes?

nothing​% ​(Round to one decimal place as​ needed.)

Applying mathematical operations with the remaining parts, you could have 1 more kit if you had A.1 more marker and 1 more die.

Using mathematical operations of divisions, subtractions, and additions, we can determine the number of kits made from the materials and the part required to make one additional kit.

For instance, 287 people marker can make 47 (287/6) kits with 5 remaining, which requires another 1 part to complete another kit.

143 6-sided die can also make 47 kits (143/3) with 2 parts, which require an additional 1 part to make another kit.

The above parts are unlike the teleporter marker, which had already made 48 kits with 5 of its part remaining.

Part                     Number in each kit    Number available   # of Kits Made

People marker                   6                            287                      47

6-sided die                         3                            143                      47

Teleporter marker             7                            341                      48

Thus, using mathematical operations, we can determine that to complete the number of kits to 48, the kit maker requires Option A.

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Using proportional relationships, we have that:

a) They are defined as follows:

b) The relation is Out of State Team = 1/5 x Residents.

A graph represents a proportional relationship if the output variable y in the y-axis is written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:

y = kx.

Voice instructor notices that only one out of every ten of her students can sing soprano, hence the constant is:

k = 1/10 = 0.1.

Then the relationship is:

Soprano = 0.1 x Students.

Two out of every six vehicles are trucks, hence the constant is:

k = 2/6 = 1/3.

Hence the relationship is:

Trucks = 1/3 x Vehicles.

Then, in item b, we want to write a relation that has a constant between those represented on the previous relations, that is, between 1/10 and 1/3.

One possible constant is of 1/5. Supposing that one out of five New York City residents root for out of state NFL teams, the relation is:

Out of State Team = 1/5 x Residents.

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The digits at ones place are 8 and the hundredth place is 9.

The number which is left to the decimal is considered in one's places as proceeding with the numbers tens places and the hundredth place is obtained. Similarly on the right side moving towards the right gives tenth place and hundredth place.

18.09

(1) - It is in the Tens place

(8) - Ones place

(.) - Decimal point

(0) - Tenth place

(9) Hundredth place

Therefore, The digits at one place are 8 and the hundredth place is 9.

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solution

To factorize the Trinomial, we seek two numbers such that the product is -14 and the addition is 5

We have

Pair Product sum

(-2, 7) -14 5

Hence we have

Hence the correct option is C

In 1820  different ways a group of four people can be selected from this group of 16.

In 35 ways four women can be chosen from the group of 7 women.

The probability that all women will be chosen to attend the conference is 1.92%.

The proportion of favourable outcomes to all possible outcomes of an event is known as the probability. The number of positive outcomes for an experiment with 'n' possible outcomes can be represented by the symbol x. The probability of an event can be determined using the following formula.

To find how many different ways can a group of four people be selected from this group of 16, we will implement the combination formula.

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

Where,

nCr = number of combinations

n = total number of objects in the set

r = number of choosing objects from the set

Here, n = 16 and r = 4, substituting the values we get

[tex]^{16} C_4=\frac{16 !}{4 ! (16-4) !}[/tex]

[tex]^{16} C_4 =[/tex] 1820

Hence, in 1820  different ways a group of four people can be selected from this group of 16.

To find how many ways can four women be chosen from the group of 7 women we will implement the combination formula.

Here, n = 7 women and r  = 4 women, substituting the values we get

[tex]^7 C_4=\frac{7 !}{4 ! (7-4) !}[/tex]

[tex]^7 C_4=[/tex] 35

Thus, in 35 ways four women can be chosen from the group of 7 women.

The probability that all women will be chosen to attend the conference is

[tex]\frac{^7 C_4}{^{16}C_4}[/tex] = 35/1820

       = 0.01923076

       = 1.92%

Thus, the probability that all women will be chosen to attend the conference is 1.92%.

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Answer:

x = 2√174, -2√174

x ≈ 26.38

Step-by-step explanation:

23² + x² = 35²

529 + x² = 1225

-529         -529

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

x² = 696

√x² = √696

x = 2√174, -2√174

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

b = √c² - a²

b = √35² - 23²

b ≈ 26.38

I hope this helps!

1. First we find the product of 3 and 6. Product=addition

3+6=8

8 is the product of 3 and 6.

2. Now we find the difference between 8 and the square root of 36.

The square root of 36 is 6. (6x6=36)

8-6=2.

3. Now we must divide 36 by 2.

36/2=18.

ANSWER= 18

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

these are a bit complicated, but i hope that helped!! the tricky part is breaking it up and trying to find which goes first.- || much love! <33

Dividing 36 by the difference between product of 3 and 6 and the square root of 36 gives 3.

The problem asks us to divide 36 by the difference between the product of 3 and 6 and the square root of 36.

First, we need to find the product of 3 and 6, which is 18.

Then, we need to find the square root of 36, which is 6.

So, the difference between the product of 3 and 6 and the square root of 36 is 18 - 6 = 12.

Therefore, we need to divide 36 by 12.

We can do this by performing long division, or by using the calculator.

The answer is 3.

Here is the long division solution:

36 / 12 = 3

Here is the calculator solution:

36 / 12 = 3

Therefore, the answer to the problem is 3.

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Answer: 9.73

Step-by-step explanation:

the five at the end indicates rounding up so the answer for the 2 decimal places is 9.73.

Answer:

9.73

Rule #1: If the last digit in 9.725 is less than 5, then remove the last digit.

Rule #2: If the last digit in 9.725 is 5 or more and the second to the last digit in 9.725 is less than 9, then remove the last digit and add 1 to the second to the last digit.

Rule #3: If the last digit in 9.725 is 5 or more and the second to the last digit in 9.725 is 9, and the third to the last digit is less than 9, then remove the last digit, make the second to last digit 0, and add 1 to the number to the third to the last digit.

Rule #4: If the last digit in 9.725 is 5 or more and the second to the last digit is 9, and the third to the last digit is 9, then add 1 to the number on the left side of the decimal point and make the right side of the decimal point 00.

When rounding 9.725 to two decimal places we use Rule #2. Therefore, the answer to "What is 9.725 rounded to 2 decimal places?" is:

Answer:

See picture

Step-by-step explanation:

Answer:5.44

Step-by-step explanation:

3.2x1.7

This can be re-inserted into our vertex equation to obtain. y=2(x−2)2+3.

In "standard form," if your instructor desires it, we can expand the right side to get:

Write a quadratic function with a vertex of (2, "-3)" to show results

Find write a quadratic function with vertex of instead (2, -3)

Answer 1

A quadratic's common vertex form is. y=m(x−a)2+b.

In light of the vertex, this becomes (2,3).

So, we do. 11=m(4−2)2+3. f(x) = a(x - h)2 + k, where a, h, and k are constants, is the vertex form of a quadratic function (h, k). If the vertex form of the quadratic parent function f(x) = x2 is used, then y = a(x - h)2 + k, where a = 1, h = 0, and k = 0.

Putting it simply: 8=m(2)2. 8=4m. m=2.

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Answer:

1/5

Step-by-step explanation:

Finding the unknown value in exponent form:

Prime factorize 125.

      125 = 5 * 5 * 5 = 5³

   [tex]\sf k^3 = \dfrac{1}{125}\\\\ k^3 = \left(\dfrac{1}{5}\right)^3[/tex]

As exponents are same, compare the bases,

 [tex]\sf k = \dfrac{1}{5}[/tex]

Answer:

x=1/5

Step-by-step explanation:

[tex]k^3=1/125\\[/tex]

[tex](k^3)^\frac{1}{3} =(\frac{1}{125} )^\frac{1}{3}[/tex]

 [tex]k^3^\frac{1}{3} =\frac{1}{125^\frac{1}{3}}[/tex]

[tex]k=\frac{1}{5}[/tex]

Hope this Helps :)

For the first function, the coordinates of A are (0, 1).

The equation of circle B is (x -4)^2 + y^2 = 25

And the circle intercepts the x-axis at:

(9, 0) and (-1, 0)

We have the equation:

y = a^x

And we know that A is the y-intercept of that equation, remember that the y-intercept is the point such that x = 0, so the y-coordinate will e:

y = a^0 = 1

So the y-intercept (point A)  is the point (0, 1).

We start with the circle:

x^2 + y^2 = 25

And we apply a translation of 4 units to the right, so we write this as:

(x - 4)^2 + y^2  = 25

c) The circle intercepts the x-axis when y = 0, then:

(x - 4)^2 + 0^2 = 25

x - 4 = ±√25

x - 4 = ±5

x = 4 ± 5

Then the two points where the circle intercepts the x-axis are:

(9, 0) and (-1, 0)

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Answer:

77/12

Step-by-step explanation:

3 3/4 + 2 2/3

15/4+8/3

45/12+32/12

77/12

Answer:

Step-by-step explanation: $3.02

3 pounds difference

The complete table will be;

In 2 years, The amount of salary = $35,200

In 5 years, The amount of salary = $31,200 + 5 x $4,000 =  $51,200

In 10 years, The amount of salary = $71,200

In x years, The amount of salary =  =  $31,200 + $4,000x

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A high school graduate can make $31,200 per year.

Any additional year of training or schooling can increase the salary by $4,000 per year.

Now, In one year, Salary = $31,200

So, In 2 years, The amount of salary = $31,200 + $4,000

                                                        = $35,200

In 5 years, The amount of salary = $31,200 + 5 x $4,000

                                                  = $31,200 + $20,000

                                                  = $51,200

In 10 years, The amount of salary = $31,200 + 10 x $4,000

                                                   = $31,200 + $40,000

                                                   = $71,200

In x years, The amount of salary = $31,200 + x × $4,000

                                                  = $31,200 + $4,000x

Thus, The complete table will be;

In 2 years, The amount of salary = $35,200

In 5 years, The amount of salary = $31,200 + 5 x $4,000 =  $51,200

In 10 years, The amount of salary = $71,200

In x years, The amount of salary =  =  $31,200 + $4,000x

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Isaac need to invest $ 36720.

Given,

Isaac is going to invest in an account paying an interest rate of 6.3% compounded monthly.

and,  the value of the account to reach $57,000 in 7 years.

To find the how much would Isaac need to invest.

Now, According to the question:
Let x be the invest in an account.

Based on the given conditions,

formulate:

x . [tex]([/tex]1 + 6.3%/ 12[tex])^7^.^1^2[/tex] = 57000

Solve the equation

x . (1 + 0.063/12[tex])^7^.^1^2[/tex] = 57000

Convert decimals to integers

x . (1 + 63/12000[tex])^7^.^1^2[/tex] = 57000

Reduce the fraction

x . (1 + 21/4000[tex])^7^.^1^2[/tex] = 57000

x . ([tex]\frac{4000+21}{4000})^8^4[/tex] = 57000

Calculate the sum or difference

x . (4021 / 4000[tex])^8^4[/tex] = 57000

x = [tex]\frac{57000}{(\frac{4021}{4000})^8^4 }[/tex]

Simplify using exponent rule with same exponent :

[tex](ab)^n = a^n . b^n[/tex]

x = [tex]\frac{57000 . 4000^8^4}{4021^8^4}[/tex]

Solve the above equation, we get

x = 36720

Hence, Isaac need to invest $ 36720

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